Derivatives Flashcards
Describe how the value of a European option can be analyzed as the present value of the option’s expected payoff at expiration.
Describe how a delta hedge is executed.
Calculate and interpret the no-arbitrage value of interest rate for equity swaps.
Describe swaptions.
Calculate the no-arbitrage value of a European option at a node.
Interpret components of the BSM model as applied to call options in terms of the stock price and strike price at expiration (most common).
Describe the value of a call and a put.
The value of a call includes the intrinsic value and a time value. The intrinsic value is:
cT = Max[0,(ST−X)]
pT = Max[0,X−ST]
Describe the value of a call and a put. Identify put call parity equations.
The put-call parity equations are:
c + PV(X) = p + S
∴
p = c + PV(X) − S
Describe and interpret the binomial option valuation model.
The model is a lattice-based (discrete time) process for finding the probabilistic option value from each previous step given up or down values. Calculations assume a no-arbitrage approach between the option value and h shares of stock plus financing.
At each node, option value can increase by some factor u or down by some factor d equal to (1 + %Δ).
Describe floating-for-floating currency swaps.
Describe the BSM model is used to value European options on equities and currencies.
Identify the statistical process assumptions of the Black-Scholes-Merton option valuation model.
Describe the hedge ratio used to calculate the value of a European option using the binomial valuation model.
The hedge ratio h identifies the percentage of a call with price c required to offset movements in the underlying share of stock with price S. Call prices are related to movements in the underlying, so h must be non-negative. Put ratios may be negative.
Define implied volatility and explain how it is used in options trading.
Describe and compare how interest rate and equity swaps are priced and valued.
Calculate the risk neutral probability of an up or down move.
Describe how the Black model is used to value European swaptions.
The Black model determines the present value of the swaps, and then discounts them for the period until option expiry.
Interpret components of the BSM model as applied to call options in terms of a leveraged position in the underlying (alternative).
Interpret option measure theta.
Calculate and interpret the no-arbitrage value of equity, interest rate, fixed income, and currency forward and futures contracts.
(Short version)
Describe how a delta hedge is executed.
(Math version)
Describe the arbitrage possibilities if the no-arbitrage pricing framework is violated.
Explain the components of the Black model in terms of a leveraged position in the underlying.
Calculate the no-arbitrage value of a European option using a two-period binomial model.
Calculate the value of a European option at successive nodes using the binomial option valuation model.
Describe and compare how equity, interest rate, fixed income, and currency forward and futures contracts are priced and valued.
(Nonmath version)
Describe how the Black model is used to value European interest rate options and European Swaptions.
(Math version)
Calculate the hedge ratio in the binomial options model.
Describe how the black model is used to value European interest rate options and European Swaptions.
Describe an arbitrage related to option values determined using the binomial model.
From a market perspective, if the market price of the option is less (more) expensive than the synthetic price, buy (sell) the market call and sell (buy) the synthetic.
Describe forward commitments.
Describe how the Black model is used to value options of forward contracts and futures.
Mathematically state put-call parity using the Black model for forward contracts and futures.
Describe how the Black model is used to value European Swaptions.
(Math version)
Interpret option measure vega
Describe how equity and fixed-income forward and futures contracts are priced.
Interpret option measure delta.
Calculate and interpret the values of an interest rate option using a two-period binomial model.
Describe an interest rate forward agreement (FRA).
Describe how interest rate forward and futures contracts are priced.
Explain the self-financing concept of binomial model option valuation.
Calculate and interpret the no-arbitrage value of interest rate forward and futures contracts a certain number of days after initiation.
Explain the discount required in an FRA with advanced set, advanced settled features.
Give the equation used to calculate the value of a pay-return-on-one-equity-instrument, receive-return-on-another-equity-instrument swap.
Describe rho.
Calculate the value of an up or down move.
Identify other assumptions of the Black-Scholes-Merton option valuation model that are different from those for the binomial model.
Interpret option measure gamma. Describe the role of gamma risk in options trading.
Option gamma measures the curvature in the option price–stock price relationship; that is, percentage delta change given a small change in the value of the underlying stock.
Stock prices frequently change prices radically rather than smoothly as required for the BSM model; that is, they “jump.” Gamma risk describes the potential risk of being improperly hedged against large jumps.
Explain how American option valuation is different.
Describe an equity swap.
Describe and compare how equity, interest rate, fixed income, and currency forward and futures contracts are priced and valued.
(Math version)
Identify how equity swaps are different from other swaps.
Describe a contingent claim
Identify assumptions of the Black-Scholes-Merton option valuation model that are similar to those for the binomial model.
European-style options on liquid underlying instruments (with known, underlying yield where applicable); no short-selling constraint; no market frictions, such as transactions costs, taxes, or regulation; no arbitrage opportunities exist; known, constant risk-free rates; and volatility is known and constant, although different.
Explain calculations for an option using a two-period binomial model.
