Section 11.1 gives an example of a situation where the value...

Name: Problem 31, Chapter 11: Options, Futures, and Other Derivatives
Uploaded: 2024-10-01T13:57:09-08:00
Duration: 4 min 10 s
Channel: Narayan Hari
Description: Section 11.1 gives an example of a situation where the value of a European call option decreases as the time to maturity is increased. Give an example of a situation where the same thing happens for a European put option.

Section 11.1 gives an example of a situation where the value of a European call option decreases as the time to maturity is increased. Give an example of a situation where the same thing happens for a European put option.

Key Concepts

European Options

European options are financial derivatives that give the holder the right, but not the obligation, to buy (in the case of a call) or sell (in the case of a put) an underlying asset at a predetermined strike price only at the option's expiration date. This fixed exercise date differentiates them from American options, where early exercise is allowed.

Time Value of Options

The time value of an option represents the premium above the intrinsic value that the market is willing to pay due to the possibility of favorable price movements before expiration. Typically, a longer time to maturity increases this time value since there is more opportunity for beneficial movements in the underlying asset's price. However, under special circumstances, changes in factors such as discount rates or other market conditions can reverse this effect, leading to cases where a longer maturity reduces the option's value.

Put-Call Parity

Put-call parity is a fundamental relationship in options pricing that links the prices of European call and put options with the same strike price and expiration. It expresses the put price in terms of the call price, the underlying asset's price, and the discounted strike price. Consequently, any unusual behavior in the call price as a function of time to maturity can be translated into corresponding effects on the put price.

Interest Rate and Discounting Effects

Interest rates have a major influence on option pricing through the discount factor applied to the strike price. With a high interest rate environment, the present value of the strike price decreases more significantly as the time to maturity increases. This can outweigh the added time value of the option, potentially leading to situations where the value of a European put option (or call option) decreases as the time to maturity increases, because the discounted strike price component diminishes with longer maturities.

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