Chapter 4
European Currency Option Analytics
The previous chapter developed the industry-standard Black-Scholes-Merton (BSM) model for European currency options. Attention now turns to using the model to understand the dynamics of option valuation and the analysis of option risk.
BASE-CASE ANALYSIS
In the BSM model, five factors contribute to the valuation of a currency option: The spot exchange rate, the market level of option volatility, the foreign interest rate, the domestic interest rate, and the time to expiration. One way to get a fast look at how these factors work is to examine the change in an option's value when each factor by itself is subject to a small change. Exhibit 4.1 does this experiment on the one-month dollar put/yen call from Chapter 3. Under the base-case assumptions, this option is worth $27,389. When the pricing factors change, the dynamics are as follows:
- A one-yen move in the spot exchange up from 90 to 91 removes $5,234 of value from the option.
- One day of time decay costs the holder of the option $190 as the time to expiration shrinks from 90 days to 89 days.
- A one percent increase in market option volatility, meaning a rise from 14 percent to 15 percent, adds $1,955 to the value of the option.
- An increase in the foreign interest rate by 1 percent, from 2 percent to 3 percent, subtracts $1,233 from the option value.
- An increase in the domestic interest rate by 1 percent, from 5 percent to 6 percent, adds $1,200 to the value of the option.
