Suppose that a central bank's policy is to allow an exchange...

Name: Problem 11, Chapter 20: Options, Futures, and Other Derivatives
Uploaded: 2021-02-06T20:10:22-08:00
Duration: 48 s
Channel: Majid Borumand
Description: Suppose that a central bank's policy is to allow an exchange rate to fluctuate between 0.97 and 1.03 . What pattern of implied volatilities for options on the exchange rate would you expect to see?

Suppose that a central bank's policy is to allow an exchange rate to fluctuate between 0.97 and 1.03 . What pattern of implied volatilities for options on the exchange rate would you expect to see?

Key Concepts

Exchange Rate Target Zone

This concept refers to a regime where a central bank commits to keeping its currency’s exchange rate within a predetermined band. The existence of such a target zone influences market expectations because it effectively caps how far the exchange rate can deviate, thereby altering the underlying asset’s risk profile compared to an unconstrained process.

Central Bank Intervention

Central bank intervention is the mechanism by which a monetary authority acts in the foreign exchange market to enforce or maintain the target zone. This intervention, either through buying or selling its own currency, reduces the likelihood of extreme outcomes and thereby affects the statistical distribution of future exchange rates.

Implied Volatility in Option Pricing

Implied volatility represents the market’s forecast of the exchange rate’s future volatility, as extracted from option prices. It is a key parameter in option pricing models, such as Black-Scholes, and adjustments in its estimation reflect changes in the perceived risk, particularly when the underlying asset’s return distribution is altered by external constraints or policies.

Volatility Smile/Skew

The volatility smile (or skew) describes the pattern typically observed when implied volatility is plotted against option strike prices. In a constrained environment like a target zone, market participants expect lower volatility for outcomes near the enforced boundaries (due to central bank intervention) relative to those further away, leading to a distinctive curve where implied volatilities are higher for strikes that lie well within or outside the target zone.

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