What is the impact (if any) of negative interest rates on:...

Name: Problem 22, Chapter 11: Options, Futures, and Other Derivatives
Uploaded: 2023-12-06T09:23:28-08:00
Duration: 5 min 30 s
Channel: Jennifer Stoner
Description: What is the impact (if any) of negative interest rates on: (a) The put-call parity result for European options (b) The result that American call options on non-dividend-paying stocks should never be exercised early (c) The result that American put options on non-dividend-paying stocks should sometimes be exercised early. Assume that holding cash earning zero interest is not possible.

What is the impact (if any) of negative interest rates on: (a) The put-call parity result for European options (b) The result that American call options on non-dividend-paying stocks should never be exercised early (c) The result that American put options on non-dividend-paying stocks should sometimes be exercised early. Assume that holding cash earning zero interest is not possible.

What is the impact (if any) of negative interest rates on:
(a) The put-call parity result for European options
(b) The result that American call options on non-dividend-paying stocks should never be exercised early
(c) The result that American put options on non-dividend-paying stocks should sometimes be exercised early.
Assume that holding cash earning zero interest is not possible.

Key Concepts

Negative Interest Rates

Negative interest rates occur when the nominal rate of interest is below zero, altering the standard time value of money considerations. In the context of option pricing, they affect the discount factor used in present value calculations, shifting the balance between holding cash and other assets, and thereby subtly influencing arbitrage relationships and early exercise decisions.

Put?Call Parity for European Options

Put-call parity is a fundamental relationship that links the prices of European call and put options with the same strike and expiration by incorporating the underlying asset's current price and the discounted strike price. With negative interest rates, the discount factor for the strike price increases rather than decreases as in the positive rate case, thus modifying the balance in the traditional parity relationship and its interpretation.

Early Exercise of American Call Options on Non?Dividend-Paying Stocks

For options on non-dividend-paying stocks, it is generally suboptimal to exercise American call options early because doing so forfeits the time value of the option. Negative interest rates influence the benefit of holding the option versus outright ownership, but since there is no dividend benefit from holding the stock, the fundamental argument against early exercise generally holds, although the incentive adjustments might be slightly affected by the cost-of-carry considerations under negative rates.

Early Exercise of American Put Options on Non?Dividend-Paying Stocks

In the case of American put options, early exercise can sometimes be optimal because the put option may be deep in the money and the benefit of receiving cash sooner can outweigh the loss of remaining time value. With negative interest rates, the benefit of immediate cash flows is more pronounced since the traditional time value discounting is reversed, potentially increasing the attractiveness of early exercise in certain scenarios.

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