18

Option Pricing and Risks

This chapter reviews the main inputs to pricing an option using the Black-Scholes model and considers how changes in the inputs affect the outputs. The model itself is described in Chapter 17. This chapter focuses on the sensitivity of the option value to changes in the key input assumptions - the price of the underlying; the time to expiry; volatility; and the cost of carrying a hedge position in the underlying. It explores the so-called option ‘Greeks’: delta, gamma, theta, vega, and rho. The chapter looks at how traders can use these measures to manage the risks on option positions by trading in the underlying, and the circumstances when hedges are more or less efficient. The body of the chapter looks at how traders manage ‘delta exposures’: potential losses on option positions that arise from changes in the value of the underlying. This is explored in more detail in an Appendix, with a description of how the gamma exposure on an option position can be hedged.

The value of an option consists of intrinsic value plus time value. For a call, intrinsic value is the maximum of zero and the price of the underlying minus the strike. For a put, it is the maximum of zero and the strike minus the price of the underlying. Other things being equal, the time value of an option tends to be greater:

• the longer the time remaining until expiry;

• the greater the volatility of the underlying asset. ...

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