Curriculum map

The ordered lesson path is generated from the track and lesson records; the atomic graph is generated from competency records. Sidebar position does not define prerequisites—directed prerequisites, requires, and teaches references do.

Bond derivatives foundations

A path from deterministic present value and no-arbitrage through forwards, vanilla options, bond settlement, lattice valuation, European bond options, and issuer-default knockout.

Audience: Learners comfortable with basic algebra, percentages, and exponents; probability, risk-neutral pricing, and credit survival are introduced in the track.

Entry assumptions:

Basic algebra
Percentages and decimal notation
Integer exponents

Lesson 1
Cash-flow timelines and perspective
foundations.cash-flow-timelines
Place signed payments on one time axis before valuing them.
Requires
Track entry assumptions only
Teaches
finance.cash-flow-timeline.interpretfinance.cash-flow-perspective.apply
Evidence
cash-flow-timelines-check
Lesson 2
Events, conditional probability, and expectation
foundations.probability-events-and-expectation
Calculate expected values from disjoint events, including values that vary inside an event.
Requires
Track entry assumptions only
Teaches
probability.events.interpretprobability.conditional-probability.calculateprobability.expectation-by-partition.calculate
Evidence
probability-events-expectation-check
Lesson 3
Rate quotes, compounding, and basis points
foundations.rates-compounding-and-basis-points
Separate an annualized quote from its periodic rate and its units.
Requires
Track entry assumptions only
Teaches
rates.nominal-rate-quote.interpretrates.periodic-rate.calculaterates.basis-points.convert
Evidence
rates-compounding-check
Lesson 4
Discount factors
foundations.discount-factors
Convert one deterministic future unit into its value at time zero.
Requires
rates.periodic-rate.calculate
Teaches
rates.discount-factor.interpretrates.discount-factor.calculate
Evidence
discount-factor-check
Lesson 5
Present value of a cash-flow schedule
foundations.present-value
Discount each signed dated amount and then add the comparable values.
Requires
finance.cash-flow-perspective.applyrates.discount-factor.calculate
Teaches
finance.present-value.interpretfinance.present-value.calculate
Evidence
present-value-check
Lesson 6
No-arbitrage and replication
foundations.no-arbitrage-and-replication
Match every dated state-contingent cash flow before using one portfolio to value another.
Requires
finance.cash-flow-perspective.applyfinance.present-value.interpret
Teaches
finance.law-of-one-price.explainfinance.replicating-portfolio-value.calculate
Evidence
no-arbitrage-replication-check
Lesson 7
Risk-neutral pricing is not a risk-free probability
foundations.risk-neutral-pricing
Separate real-world forecasts from no-arbitrage pricing weights, then discount a finite-state expected payoff.
Requires
finance.law-of-one-price.explainfinance.present-value.calculatefinance.present-value.interpretprobability.expectation-by-partition.calculate
Teaches
finance.risk-neutral-measure.interpretfinance.risk-neutral-value.calculate
Evidence
risk-neutral-pricing-check
Lesson 8
Discount curve and forward discounting
rates.discount-curve-and-forward-discounting
Move from one discount factor to a dated deterministic curve and derive future-to-future discount factors.
Requires
rates.discount-factor.calculaterates.discount-factor.interpret
Teaches
rates.discount-curve.interpretrates.forward-discount-factor.calculate
Evidence
discount-curve-check
Lesson 9
Fixed-rate bond contract and cash flows
bonds.fixed-rate-contract-and-cash-flows
Translate face value, coupon rate, frequency, and maturity into promised payments.
Requires
finance.cash-flow-perspective.applyrates.nominal-rate-quote.interpret
Teaches
bonds.fixed-rate-contract.interpretbonds.coupon-amount.calculatebonds.fixed-cashflows.identify
Evidence
bond-contract-cash-flows-check
Lesson 10
Bond price from discount factors
bonds.price-from-discount-factors
Apply one discount factor to each promised payment before adding.
Requires
bonds.fixed-cashflows.identifyfinance.present-value.calculate
Teaches
bonds.price-from-discount-factors.calculate
Evidence
bond-discount-factor-price-check
Lesson 11
Yield to maturity as a single-rate summary
bonds.yield-to-maturity
Interpret the rate that reproduces a toy bond price, then calculate the price from an input yield.
Requires
bonds.price-from-discount-factors.calculaterates.periodic-rate.calculate
Teaches
bonds.yield-to-maturity.interpretbonds.price-from-yield.calculate
Evidence
bond-yield-check
Lesson 12
Settlement, accrued interest, and clean versus dirty price
bonds.settlement-clean-and-dirty-price
Calculate actual/actual coupon-period accrual and keep quoted and cash bond prices on one basis.
Requires
bonds.fixed-cashflows.identifyfinance.cash-flow-timeline.interpret
Teaches
bonds.clean-dirty-price.calculate
Evidence
bond-settlement-check
Lesson 13
Forward contracts, delivery price, and value
derivatives.forward-contracts-and-value
Separate a forward's obligation, fair delivery price, and changing signed contract value.
Requires
finance.cash-flow-perspective.applyfinance.law-of-one-price.explainfinance.present-value.calculaterates.discount-factor.calculate
Teaches
derivatives.forward-contract.interpretderivatives.forward-delivery-price.calculatederivatives.forward-value.calculate
Evidence
forward-contracts-value-check
Lesson 14
Bond forwards
bonds.bond-forwards
Apply cash-and-carry to a coupon bond while keeping coupon ownership and dirty-price units explicit.
Requires
bonds.clean-dirty-price.calculatebonds.price-from-discount-factors.calculatederivatives.forward-delivery-price.calculate
Teaches
bonds.forward-delivery-price.calculate
Evidence
bond-forward-check
Lesson 15
European option contracts and payoffs
derivatives.european-option-contracts-and-payoffs
Separate call and put rights from expiry payoff, current value, premium, and profit.
Requires
finance.cash-flow-perspective.applyfinance.present-value.interpret
Teaches
options.european-contract.interpretoptions.payoff.calculateoptions.value-payoff-profit.distinguish
Evidence
european-option-contracts-payoffs-check
Lesson 16
Put-call parity and synthetic forwards
derivatives.put-call-parity
Match European call and put portfolios state by state before solving a missing value.
Requires
derivatives.forward-contract.interpretderivatives.forward-delivery-price.calculatefinance.law-of-one-price.explainoptions.payoff.calculate
Teaches
options.put-call-parity.explainoptions.put-call-parity.calculate
Evidence
put-call-parity-check
Lesson 17
One-period binomial option valuation
derivatives.one-period-binomial-option-valuation
Price two-state option payoffs by both exact replication and risk-neutral weighting.
Requires
finance.replicating-portfolio-value.calculatefinance.risk-neutral-value.calculateoptions.payoff.calculate
Teaches
options.binomial-hedge.calculateoptions.one-period-binomial-value.calculate
Evidence
one-period-binomial-option-check
Lesson 18
Multi-period lattice valuation
derivatives.multiperiod-lattice-valuation
Extend one-period risk-neutral valuation to node-by-node backward induction with local discount factors.
Requires
finance.risk-neutral-value.calculateoptions.one-period-binomial-value.calculate
Teaches
finance.backward-induction.calculate
Evidence
multiperiod-lattice-check
Lesson 19
European bond options
bond-options.european-bond-options
Define a standalone option on a bond, put its prices on one cash-price basis, and value expiry payoffs on an input lattice.
Requires
bonds.clean-dirty-price.calculatefinance.backward-induction.calculateoptions.european-contract.interpretoptions.payoff.calculate
Teaches
bond-options.contract.interpretbond-options.european-value.calculate
Evidence
bond-option-check
Lesson 20
Default, hazard, and survival
credit.default-hazard-and-survival
Read an input survival curve, calculate interval default probabilities, and use a constant-hazard toy model.
Requires
finance.cash-flow-timeline.interpretfinance.risk-neutral-measure.interpretprobability.conditional-probability.calculateprobability.events.interpret
Teaches
credit.survival-probability.interpretcredit.default-probability-from-survival.calculatecredit.hazard-rate.interpretcredit.survival-from-constant-hazard.calculate
Evidence
credit-default-survival-check
Lesson 21
Recovery and one-period risky present value
credit.recovery-and-risky-present-value
Value a narrowly defined recovery-of-par claim whose survival and default-state payments both occur at maturity.
Requires
credit.default-probability-from-survival.calculatefinance.cash-flow-perspective.applyfinance.present-value.calculatefinance.risk-neutral-value.calculateprobability.expectation-by-partition.calculate
Teaches
credit.recovery-rate.interpretcredit.loss-given-default.calculatecredit.risky-present-value.calculate
Evidence
credit-recovery-risky-pv-check
Lesson 22
Issuer-default knockout bond options
bond-options.issuer-default-knockout
Value a bond option that is extinguished by issuer default while keeping bond recovery separate.
Requires
bond-options.contract.interpretbond-options.european-value.calculatecredit.recovery-rate.interpretcredit.survival-probability.interpretfinance.backward-induction.calculate
Teaches
bond-options.default-knockout.interpretbond-options.default-knockout-value.calculate
Evidence
default-knockout-bond-option-check

Credit products foundations

A first path from events and discounted expectations through bonds, credit survival, exact-time CDS legs, and quote/upfront conversion.

Audience: Learners comfortable with basic algebra, percentages, and exponents; probability and risk-neutral pricing are introduced in the track.

Entry assumptions:

Basic algebra
Percentages and decimal notation
Integer exponents

Lesson 1
Cash-flow timelines and perspective
foundations.cash-flow-timelines
Place signed payments on one time axis before valuing them.
Requires
Track entry assumptions only
Teaches
finance.cash-flow-timeline.interpretfinance.cash-flow-perspective.apply
Evidence
cash-flow-timelines-check
Lesson 2
Events, conditional probability, and expectation
foundations.probability-events-and-expectation
Calculate expected values from disjoint events, including values that vary inside an event.
Requires
Track entry assumptions only
Teaches
probability.events.interpretprobability.conditional-probability.calculateprobability.expectation-by-partition.calculate
Evidence
probability-events-expectation-check
Lesson 3
Rate quotes, compounding, and basis points
foundations.rates-compounding-and-basis-points
Separate an annualized quote from its periodic rate and its units.
Requires
Track entry assumptions only
Teaches
rates.nominal-rate-quote.interpretrates.periodic-rate.calculaterates.basis-points.convert
Evidence
rates-compounding-check
Lesson 4
Discount factors
foundations.discount-factors
Convert one deterministic future unit into its value at time zero.
Requires
rates.periodic-rate.calculate
Teaches
rates.discount-factor.interpretrates.discount-factor.calculate
Evidence
discount-factor-check
Lesson 5
Present value of a cash-flow schedule
foundations.present-value
Discount each signed dated amount and then add the comparable values.
Requires
finance.cash-flow-perspective.applyrates.discount-factor.calculate
Teaches
finance.present-value.interpretfinance.present-value.calculate
Evidence
present-value-check
Lesson 6
No-arbitrage and replication
foundations.no-arbitrage-and-replication
Match every dated state-contingent cash flow before using one portfolio to value another.
Requires
finance.cash-flow-perspective.applyfinance.present-value.interpret
Teaches
finance.law-of-one-price.explainfinance.replicating-portfolio-value.calculate
Evidence
no-arbitrage-replication-check
Lesson 7
Risk-neutral pricing is not a risk-free probability
foundations.risk-neutral-pricing
Separate real-world forecasts from no-arbitrage pricing weights, then discount a finite-state expected payoff.
Requires
finance.law-of-one-price.explainfinance.present-value.calculatefinance.present-value.interpretprobability.expectation-by-partition.calculate
Teaches
finance.risk-neutral-measure.interpretfinance.risk-neutral-value.calculate
Evidence
risk-neutral-pricing-check
Lesson 8
Discount curve and forward discounting
rates.discount-curve-and-forward-discounting
Move from one discount factor to a dated deterministic curve and derive future-to-future discount factors.
Requires
rates.discount-factor.calculaterates.discount-factor.interpret
Teaches
rates.discount-curve.interpretrates.forward-discount-factor.calculate
Evidence
discount-curve-check
Lesson 9
Fixed-rate bond contract and cash flows
bonds.fixed-rate-contract-and-cash-flows
Translate face value, coupon rate, frequency, and maturity into promised payments.
Requires
finance.cash-flow-perspective.applyrates.nominal-rate-quote.interpret
Teaches
bonds.fixed-rate-contract.interpretbonds.coupon-amount.calculatebonds.fixed-cashflows.identify
Evidence
bond-contract-cash-flows-check
Lesson 10
Bond price from discount factors
bonds.price-from-discount-factors
Apply one discount factor to each promised payment before adding.
Requires
bonds.fixed-cashflows.identifyfinance.present-value.calculate
Teaches
bonds.price-from-discount-factors.calculate
Evidence
bond-discount-factor-price-check
Lesson 11
Yield to maturity as a single-rate summary
bonds.yield-to-maturity
Interpret the rate that reproduces a toy bond price, then calculate the price from an input yield.
Requires
bonds.price-from-discount-factors.calculaterates.periodic-rate.calculate
Teaches
bonds.yield-to-maturity.interpretbonds.price-from-yield.calculate
Evidence
bond-yield-check
Lesson 12
The bond price-yield relationship
bonds.price-yield-relationship
Explain why the price of fixed positive cash flows decreases when the yield increases, and why the price-yield curve is not linear.
Requires
bonds.price-from-yield.calculate
Teaches
bonds.price-yield-direction.explainbonds.price-yield-curvature.interpret
Evidence
bond-price-yield-shape-check
Lesson 13
Default, hazard, and survival
credit.default-hazard-and-survival
Read an input survival curve, calculate interval default probabilities, and use a constant-hazard toy model.
Requires
finance.cash-flow-timeline.interpretfinance.risk-neutral-measure.interpretprobability.conditional-probability.calculateprobability.events.interpret
Teaches
credit.survival-probability.interpretcredit.default-probability-from-survival.calculatecredit.hazard-rate.interpretcredit.survival-from-constant-hazard.calculate
Evidence
credit-default-survival-check
Lesson 14
Recovery and one-period risky present value
credit.recovery-and-risky-present-value
Value a narrowly defined recovery-of-par claim whose survival and default-state payments both occur at maturity.
Requires
credit.default-probability-from-survival.calculatefinance.cash-flow-perspective.applyfinance.present-value.calculatefinance.risk-neutral-value.calculateprobability.expectation-by-partition.calculate
Teaches
credit.recovery-rate.interpretcredit.loss-given-default.calculatecredit.risky-present-value.calculate
Evidence
credit-recovery-risky-pv-check
Lesson 15
CDS premium and protection legs
cds.premium-protection-legs-and-par-spread
Build exact default-time expectations for the two CDS legs and solve the zero-upfront par spread.
Requires
credit.default-probability-from-survival.calculatecredit.hazard-rate.interpretcredit.loss-given-default.calculatecredit.recovery-rate.interpretcredit.survival-from-constant-hazard.calculatecredit.survival-probability.interpretfinance.cash-flow-perspective.applyfinance.present-value.calculatefinance.risk-neutral-measure.interpretfinance.risk-neutral-value.calculateprobability.events.interpretprobability.expectation-by-partition.calculaterates.basis-points.convert
Teaches
cds.cash-flow-legs.interpretcds.premium-leg.calculatecds.protection-leg.calculatecds.par-spread.calculate
Evidence
cds-legs-par-spread-check
Lesson 16
CDS market-standard quote and upfront
cds.market-standard-quote-and-upfront
Distinguish a conventional CDS spread quote from a fixed running coupon, identify which quantity is observed and which is solved, calculate the signed upfront amount, and reverse the simplified conversion.
Requires
cds.par-spread.calculatecds.premium-leg.calculatecds.protection-leg.calculatecredit.hazard-rate.interpretcredit.survival-from-constant-hazard.calculate
Teaches
cds.market-standard-quote.interpretcds.upfront-amount.calculatecds.quote-upfront-conversion.calculate
Evidence
cds-market-standard-quote-upfront-check
Lesson 17
Credit curve and market observables
cds.credit-curve-and-market-observables
Separate what the CDS market shows from what a pricing model assumes or solves, read a credit curve as tenor marks plus a fitted survival curve, and distinguish transforming quotes from fitting the curve.
Requires
cds.market-standard-quote.interpretcds.par-spread.calculatecds.quote-upfront-conversion.calculatecds.upfront-amount.calculatecredit.hazard-rate.interpretcredit.survival-from-constant-hazard.calculatecredit.survival-probability.interpretfinance.risk-neutral-measure.interpretrates.discount-curve.interpret
Teaches
cds.market-observables.interpretcds.credit-curve.interpretcds.credit-curve-fit.calculate
Evidence
cds-credit-curve-observables-check
Lesson 18
Equivalent notional and quote risk
cds.equivalent-notional-and-quote-risk
Measure a CDS position's sensitivity to the liquid tenor's quote by bump and reprice, then size the liquid-tenor equivalent notional and equivalent ratio that offset it.
Requires
cds.cash-flow-legs.interpretcds.market-standard-quote.interpretcds.quote-upfront-conversion.calculatecds.upfront-amount.calculate
Teaches
cds.quote-sensitivity.calculatecds.equivalent-notional.calculate
Evidence
cds-equivalent-notional-check

Atomic competency catalog

Each competency has an explicit prerequisite list and an evidence policy. The build rejects unknown references, cycles, invalid lesson ordering, and insufficient assessment coverage.

The competency dependency graph: an arrow runs from a prerequisite to the competency that builds on it

Interpret a European bond option
bond-options.contract.interpret
Interpret a standalone European call or put on a named bond, including exercise time, dirty-versus-clean strike basis, coupon timing, and holder rights.
Requires: options.european-contract.interpret, bonds.clean-dirty-price.calculate
Calculate an issuer-default knockout option value
bond-options.default-knockout-value.calculate
Calculate an issuer-default knockout bond option value on an input joint rate-credit lattice by applying survival to option continuation and zero option payoff on pre-expiry default.
Requires: bond-options.default-knockout.interpret, bond-options.european-value.calculate, finance.backward-induction.calculate
Interpret an issuer-default knockout
bond-options.default-knockout.interpret
Interpret an issuer-default knockout bond option as a contract extinguished with zero option rebate if the bond issuer defaults before exercise, separately from any recovery on the bond.
Requires: bond-options.contract.interpret, credit.survival-probability.interpret, credit.recovery-rate.interpret
Calculate a European bond option value
bond-options.european-value.calculate
Calculate a European bond option payoff at expiry and value it by backward induction on an input default-free bond-value lattice.
Requires: bond-options.contract.interpret, finance.backward-induction.calculate, options.payoff.calculate
Calculate clean and dirty bond prices
bonds.clean-dirty-price.calculate
Calculate actual/actual coupon-period accrued interest and convert consistently between clean quoted price and dirty invoice price.
Requires: bonds.fixed-cashflows.identify, finance.cash-flow-timeline.interpret
Calculate a periodic coupon amount
bonds.coupon-amount.calculate
Calculate each level coupon as face value times annual coupon rate divided by payments per year.
Requires: bonds.fixed-rate-contract.interpret
Identify fixed-coupon bond cash flows
bonds.fixed-cashflows.identify
Construct the coupon and principal cash-flow schedule of a simplified fixed-rate bond.
Requires: bonds.coupon-amount.calculate
Interpret a simplified fixed-rate bond contract
bonds.fixed-rate-contract.interpret
Identify face value, annual coupon rate, coupon frequency, maturity, and principal redemption in a simplified fixed-rate bond description.
Requires: finance.cash-flow-perspective.apply, rates.nominal-rate-quote.interpret
Calculate a bond forward delivery price
bonds.forward-delivery-price.calculate
Calculate a no-arbitrage bond forward delivery price from the current dirty bond price, the present value of pre-delivery coupons, and the delivery-date discount factor.
Requires: derivatives.forward-delivery-price.calculate, bonds.clean-dirty-price.calculate, bonds.price-from-discount-factors.calculate
Price a bond from discount factors
bonds.price-from-discount-factors.calculate
Price a simplified fixed-rate bond by multiplying each promised cash flow by its stated discount factor and summing the results.
Requires: bonds.fixed-cashflows.identify, finance.present-value.calculate
Price a fixed-coupon bond from yield
bonds.price-from-yield.calculate
Price a simplified fixed-coupon bond from a nominal annual yield compounded at the coupon frequency.
Requires: bonds.yield-to-maturity.interpret
Interpret price-yield curvature
bonds.price-yield-curvature.interpret
Recognize that equal yield changes generally produce unequal price changes in the simplified fixed-cash-flow model.
Requires: bonds.price-yield-direction.explain
Explain the price-yield direction
bonds.price-yield-direction.explain
Explain why the price of positive fixed cash flows moves inversely to yield while discounting denominators remain positive.
Requires: bonds.price-from-yield.calculate
Interpret yield to maturity in the simplified model
bonds.yield-to-maturity.interpret
Interpret yield to maturity as the single nominal annual rate, compounded at coupon frequency, that reproduces price from promised cash flows in the simplified model.
Requires: bonds.price-from-discount-factors.calculate, rates.periodic-rate.calculate
Interpret CDS cash-flow legs
cds.cash-flow-legs.interpret
Interpret a CDS as running-premium payments exchanged for contingent protection, partition default into disjoint time events, and read the protection buyer's signed value as protection minus premium.
Requires: probability.events.interpret, finance.cash-flow-perspective.apply, finance.risk-neutral-measure.interpret, rates.basis-points.convert, credit.recovery-rate.interpret
Calculate a fitted credit curve's survival and repricing
cds.credit-curve-fit.calculate
Calculate the survival probability implied by fitted piecewise-constant hazard segments and verify that a tenor's standard contract reprices to its mark under the fitted curve.
Requires: cds.credit-curve.interpret, cds.quote-upfront-conversion.calculate, cds.par-spread.calculate, credit.survival-from-constant-hazard.calculate
Interpret a credit curve
cds.credit-curve.interpret
Interpret a credit curve as the term structure of standard-contract marks at quoted tenors together with the survival curve fitted to them, and distinguish a tenor-by-tenor change of quotation from a fit of one hazard term structure.
Requires: cds.market-observables.interpret, credit.survival-probability.interpret, credit.hazard-rate.interpret, rates.discount-curve.interpret
Calculate a liquid-tenor equivalent notional
cds.equivalent-notional.calculate
Calculate the notional and side of the most liquid standard CDS that offsets a position's sensitivity to the liquid tenor's quote, and express it as an equivalent ratio to the position notional.
Requires: cds.quote-sensitivity.calculate, cds.cash-flow-legs.interpret
Classify CDS market observables
cds.market-observables.interpret
Classify each quantity in a standard CDS valuation as market-observed, contractual, conventional, or model-solved, and explain why the traded upfront alone identifies the pricing-model hazard rate.
Requires: cds.market-standard-quote.interpret, cds.upfront-amount.calculate, finance.risk-neutral-measure.interpret, rates.discount-curve.interpret
Interpret a CDS market-standard quote
cds.market-standard-quote.interpret
Distinguish the lesson's market-standard quote from the fixed running coupon and explain the quote's role in a simplified CDS conversion.
Requires: cds.par-spread.calculate
Calculate a CDS par spread
cds.par-spread.calculate
Calculate the zero-upfront CDS running spread that equates the exact default-time premium- and protection-leg present-value magnitudes under one internally consistent model.
Requires: cds.premium-leg.calculate, cds.protection-leg.calculate
Calculate the CDS premium leg
cds.premium-leg.calculate
Calculate the positive premium-leg present-value magnitude from scheduled survival-contingent premiums and exact accrued premium integrated over modeled default time under the stated constant-hazard model.
Requires: cds.cash-flow-legs.interpret, credit.survival-probability.interpret, credit.default-probability-from-survival.calculate, credit.hazard-rate.interpret, credit.survival-from-constant-hazard.calculate, probability.expectation-by-partition.calculate, finance.present-value.calculate, finance.risk-neutral-value.calculate
Calculate the CDS protection leg
cds.protection-leg.calculate
Calculate the positive protection-leg present-value magnitude by integrating discounted loss-given-default over exact modeled default time under the stated constant risk-neutral hazard.
Requires: cds.cash-flow-legs.interpret, credit.default-probability-from-survival.calculate, credit.hazard-rate.interpret, credit.survival-from-constant-hazard.calculate, credit.loss-given-default.calculate, probability.expectation-by-partition.calculate, finance.present-value.calculate, finance.risk-neutral-value.calculate
Calculate a CDS position's quote sensitivity
cds.quote-sensitivity.calculate
Calculate a CDS position's signed value change for a one-basis-point rise in the liquid tenor's market-standard quote by re-solving the flat hazard rate and revaluing the position for its own side.
Requires: cds.upfront-amount.calculate, cds.quote-upfront-conversion.calculate, cds.market-standard-quote.interpret
Calculate a CDS quote from upfront
cds.quote-upfront-conversion.calculate
Calculate the market-standard quote implied by a signed upfront amount under the lesson's simplified flat-hazard conversion.
Requires: cds.upfront-amount.calculate, credit.hazard-rate.interpret, credit.survival-from-constant-hazard.calculate
Calculate a CDS upfront amount
cds.upfront-amount.calculate
Calculate the signed upfront amount that makes protection-buyer inception value zero for an input quote-implied premium annuity and fixed running coupon.
Requires: cds.market-standard-quote.interpret, cds.premium-leg.calculate, cds.protection-leg.calculate
Calculate default probability from survival
credit.default-probability-from-survival.calculate
Calculate time-zero cumulative or interval default probability from survival probabilities at stated times.
Requires: credit.survival-probability.interpret
Interpret a hazard rate
credit.hazard-rate.interpret
Interpret a hazard rate as an instantaneous conditional default intensity, measured per unit of time, among names that have survived to that time.
Requires: probability.conditional-probability.calculate, credit.survival-probability.interpret
Calculate loss given default
credit.loss-given-default.calculate
Calculate loss given default as one minus the recovery rate in the lesson's fractional recovery-of-par model.
Requires: credit.recovery-rate.interpret
Interpret recovery of par
credit.recovery-rate.interpret
Interpret the recovery rate as the fraction of par paid at maturity after default in the lesson's one-period recovery-of-par model.
Requires: finance.cash-flow-perspective.apply
Calculate one-period risky present value
credit.risky-present-value.calculate
Calculate the time-zero present value of a one-period recovery-of-par claim by probability-weighting its survival and default payoffs at maturity and applying the stated discount factor.
Requires: probability.expectation-by-partition.calculate, finance.present-value.calculate, finance.risk-neutral-value.calculate, credit.default-probability-from-survival.calculate, credit.loss-given-default.calculate
Calculate survival from constant hazard
credit.survival-from-constant-hazard.calculate
Calculate survival probability as S(0,t) = exp(-lambda t) under a stated non-negative constant hazard rate and consistent time units.
Requires: credit.hazard-rate.interpret
Interpret a survival probability
credit.survival-probability.interpret
Interpret survival probability as the modeled probability, conditional on survival at valuation time, of no default through a stated future time.
Requires: probability.events.interpret, finance.cash-flow-timeline.interpret, finance.risk-neutral-measure.interpret
Interpret a forward contract
derivatives.forward-contract.interpret
Interpret the long and short obligations, delivery time, delivery price, and signed expiry payoff of a forward contract.
Requires: finance.cash-flow-perspective.apply, finance.law-of-one-price.explain
Calculate a fair forward delivery price
derivatives.forward-delivery-price.calculate
Calculate the fair delivery price of a newly struck forward from spot value, present value of deterministic income before delivery, and the delivery-date discount factor.
Requires: derivatives.forward-contract.interpret, finance.present-value.calculate, rates.discount-factor.calculate
Calculate an existing forward's value
derivatives.forward-value.calculate
Calculate the signed value to the long of an existing forward from the current forward price, its fixed delivery price, quantity, and the delivery-date discount factor.
Requires: derivatives.forward-delivery-price.calculate
Calculate value by backward induction
finance.backward-induction.calculate
Calculate node values on an input multi-period recombining pricing lattice by risk-neutral expectation and one-period node discounting.
Requires: options.one-period-binomial-value.calculate, finance.risk-neutral-value.calculate
Apply a cash-flow sign perspective
finance.cash-flow-perspective.apply
Assign positive and negative signs to cash flows from an explicitly stated perspective.
Requires: finance.cash-flow-timeline.interpret
Interpret a cash-flow timeline
finance.cash-flow-timeline.interpret
Read the amount and timing of each cash flow from a stated valuation-time timeline.
Entry competency: no declared prerequisites.
Explain the law of one price
finance.law-of-one-price.explain
Explain why two portfolios with identical dated state-contingent cash flows must have the same value under the lesson's no-arbitrage assumptions.
Requires: finance.cash-flow-perspective.apply, finance.present-value.interpret
Calculate present value
finance.present-value.calculate
Discount and add dated deterministic cash flows to calculate present value.
Requires: finance.present-value.interpret
Interpret present value
finance.present-value.interpret
Explain present value as the valuation-time sum of discounted cash flows under stated assumptions.
Requires: finance.cash-flow-perspective.apply, rates.discount-factor.calculate
Calculate value from a replicating portfolio
finance.replicating-portfolio-value.calculate
Calculate a claim's no-arbitrage value from the current values and signed quantities of a portfolio that exactly replicates its future cash flows.
Requires: finance.law-of-one-price.explain
Interpret a risk-neutral measure
finance.risk-neutral-measure.interpret
Interpret risk-neutral probabilities as no-arbitrage pricing weights rather than real-world forecasts.
Requires: finance.present-value.interpret, probability.expectation-by-partition.calculate, finance.law-of-one-price.explain
Calculate a risk-neutral value
finance.risk-neutral-value.calculate
Calculate time-zero value from finite-state risk-neutral probabilities, signed terminal payoffs, and a deterministic discount factor.
Requires: finance.present-value.calculate, finance.risk-neutral-measure.interpret
Calculate a one-period replicating hedge
options.binomial-hedge.calculate
Calculate the underlying units and risk-free cash position that replicate a claim's two one-period state payoffs.
Requires: finance.replicating-portfolio-value.calculate, options.payoff.calculate
Interpret a European option contract
options.european-contract.interpret
Identify the underlying, call or put right, holder and writer, strike, expiry, and settlement perspective of a European option.
Requires: finance.cash-flow-perspective.apply
Calculate a one-period binomial option value
options.one-period-binomial-value.calculate
Calculate a European option's one-period binomial value using model-implied risk-neutral weights and deterministic discounting.
Requires: finance.risk-neutral-value.calculate, options.payoff.calculate, finance.replicating-portfolio-value.calculate
Calculate a European option payoff
options.payoff.calculate
Calculate the expiry payoff of a long or short European call or put from the underlying expiry value, strike, and quantity.
Requires: options.european-contract.interpret
Calculate a value from put-call parity
options.put-call-parity.calculate
Calculate a missing European call or put value from the other option value, prepaid forward value, strike, and expiry discount factor.
Requires: options.put-call-parity.explain, derivatives.forward-delivery-price.calculate
Explain European put-call parity
options.put-call-parity.explain
Explain European put-call parity by matching the expiry cash flows of a call-minus-put portfolio and a forward-style position under stated income and discounting assumptions.
Requires: finance.law-of-one-price.explain, derivatives.forward-contract.interpret, options.payoff.calculate
Distinguish option value, payoff, premium, and profit
options.value-payoff-profit.distinguish
Distinguish an option's current value or premium from its expiry payoff and from profit after accounting for the premium under a stated financing convention.
Requires: options.european-contract.interpret, finance.present-value.interpret
Calculate conditional probability
probability.conditional-probability.calculate
Calculate the probability of one event conditional on another positive-probability event.
Requires: probability.events.interpret
Interpret events and partitions
probability.events.interpret
Identify events and a disjoint exhaustive partition in a stated probability model.
Entry competency: no declared prerequisites.
Calculate expectation by partition
probability.expectation-by-partition.calculate
Calculate a finite expected value from event probabilities and either event values or conditional event means.
Requires: probability.events.interpret, probability.conditional-probability.calculate
Convert basis points
rates.basis-points.convert
Convert rate changes among decimal, percentage-point, and basis-point units.
Requires: rates.nominal-rate-quote.interpret
Interpret a deterministic discount curve
rates.discount-curve.interpret
Interpret a dated set of positive valuation-time discount factors as a deterministic curve, including its interpolation and no-extrapolation conventions.
Requires: rates.discount-factor.interpret
Calculate a discount factor
rates.discount-factor.calculate
Calculate D(0,T) = (1+j^(m)/m)^(-mT) from a nominal annual rate j^(m) compounded m times per year.
Requires: rates.discount-factor.interpret, rates.periodic-rate.calculate
Interpret a discount factor
rates.discount-factor.interpret
Explain a discount factor as today's value of one unit paid at a future date.
Entry competency: no declared prerequisites.
Calculate a forward discount factor
rates.forward-discount-factor.calculate
Calculate the deterministic discount factor between two future model times from their valuation-time discount factors.
Requires: rates.discount-curve.interpret, rates.discount-factor.calculate
Interpret a nominal annual rate quote
rates.nominal-rate-quote.interpret
Interpret a nominal annual rate together with its stated compounding frequency.
Entry competency: no declared prerequisites.
Calculate a periodic rate
rates.periodic-rate.calculate
Calculate the per-period rate j^(m)/m from a nominal annual rate j^(m) compounded m times per year.
Requires: rates.nominal-rate-quote.interpret