- CFA Level 2: Derivatives Part 2 – Introduction
- Introduction to Options
- Synthetic Options and Rationale
- One Period Binomial Option Pricing Model
- Call Option Price Formula
- Binomial Interest Rate Options Pricing
- Black-Scholes-Merton (BSM) Option Pricing Model
- Black-Scholes-Merton Model and the Greeks
- Dynamic Delta Hedging & Gamma Related Issues
- Estimating Volatility for Option Pricing
- Put-Call Parity for Options on Forwards
- Introduction to Swaps
- Plain Vanilla Interest Rate Swap
- Equity Swaps
- Currency Swaps
- Swap Pricing vs. Swap Valuing
- Pricing and Valuing a Plain Vanilla Interest Rate Swap
- Pricing and Valuing Currency Swaps
- Pricing and Valuing Equity Swaps
- Swaps as Theoretical Equivalents of Other Derivatives
- Swaptions and their Valuation
- Swap Credit Risk and Swap Spread
- Interest Rate Derivatives - Caps and Floors
- Credit Default Swaps (CDS)
- Credit Derivative Trading Strategies

# Put-Call Parity for Options on Forwards

An option can be created for a forward contract.

Recall that at contract initiation a forward will have a value of zero.

European options on forwards will have the same price as European options on futures contracts; but American options on forwards will have a different price from American options on futures.

The payoff values for options on forwards are:

Call payoff = Max[0,ST-X]

Put payoff = Max [0,X-ST]

ST = Underlying's price at expiration

X = Strike price of option

- Put-Call Parity for Options on Forwards:

p0 = c0 + ((X - F(0,T))/(1+rF)T)

p0 = Today's price for a European put on a futures contract

c0 = Today's price for a European call on a futures contract

X = The strike price

F(0,T) = Price at time "0" for a forward expiring at time "T"

X - F(0,T) = The face value in long position of a zero coupon bond

Excluding storage costs, F(0,T) can be substituted with the formula for pricing a forward: S0(1+rF)T

With the put call parity formula and forward pricing formula, investors can apply the put call parity relationship to exploit mispricings.

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