Bounds on Option Prices
Table of Contents
Intrinsic Value: The value of the option if it were to expire immediately (e.g. max(S - X, 0) for a call option).
Time Value: The option price minus the intrinsic value.
1 Never Exercise and American Call on a Non-Dividend Paying Stock
Consider two portfolios:
- Buy share of stock
- a. Buy zero-coupon bond with X par b. Buy call option with X strike
Payoff:
Portfolio 1:
| \(S_T > X\) | \(S_T < X\) | |
|---|---|---|
| ST | ST | ST |
| Total | ST | ST |
Portfolio 2:
| \(S_T > X\) | \(S_T < X\) | |
|---|---|---|
| C | \(S_T - X\) | 0 |
| Bond | X | X |
| Total | \(S_T\) | X |
=> We will pay more for portfolio 2.
\(C_0 + \frac{X}{1+r} > S_0 \rightarrow C_0 > max(S_0 - \frac{X}{1+r}, 0) > max(S_0 - X, 0)\)
American Call >= European Call
Non-Dividend Paying: American Call = European Call
2 What About an American Put on a Non-Dividend Paying Stock?
You may exercise the put prior to expiration. Why?
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