9.4 Forward Measure. 9.4.1 Forward Price 9.4.2 Zero-Coupon Bond as Numeraire Theorem 9.2.1.

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Presentation transcript:

9.4 Forward Measure

9.4.1 Forward Price

9.4.2 Zero-Coupon Bond as Numeraire Theorem 9.2.1

Theorem 9.2.2

9.4.3 Option Pricing with a Random Interest Rate The classical Black-Scholes-Merton formula assumes a constant interest rate. In this section, we present a generalized Black-Scholes- Merton formula that permits the interest rate to be random. the volatility of the underlying asset (constant) → the volatility of the forward price (constant) Because the forward price is a martingale under the forward measure, and is the Brownian motion used to drive asset prices under the forward measure, the assumption of constant volatility for the forward price is equivalent to the assumption

Theorem 9.2.2