Suppose that in Example 29.3 of Section 29.2 the payoff...

Name: Problem 3, Chapter 30: Options, Futures, and Other Derivatives
Uploaded: 2021-02-20T12:52:03-08:00
Duration: 1 min 34 s
Channel: Ryan Pollard
Description: Suppose that in Example 29.3 of Section 29.2 the payoff occurs after 1 year (i.e., when the interest rate is observed) rather than in 15 months. What difference does this make to the inputs to Black's model?

Suppose that in Example 29.3 of Section 29.2 the payoff occurs after 1 year (i.e., when the interest rate is observed) rather than in 15 months. What difference does this make to the inputs to Black's model?

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Key Concepts

Time to Maturity

The time to maturity in option pricing determines how long the underlying asset’s uncertainty is realized. In Black’s model, altering the payoff from 15 months to 1 year changes the period over which both risk accumulation and discounting occur, which in turn modifies the inputs such as the variance term and discount factor.

Forward Volatility

Forward volatility represents the expected variability of the underlying rate over the life of the option. By shortening the period until payoff, the relevant forward volatility is calculated over a different, typically shorter, time horizon. This impacts the option’s value since volatility is a key determinant in Black’s formula.

Discount Factor

The discount factor in Black’s model is used to present-value the expected payoff based on the risk-free rate over the time until settlement. With the payoff occurring at 1 year instead of 15 months, the discount rate is applied over a shorter duration, leading to a recalibration of the discount factor that affects the overall pricing.

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