Question

A financial institution has just sold 1,000 7-month European call options on the Japanese yen. Suppose that the spot exchange rate is 0.80 cent per yen, the exercise price is 0.81 cent per yen, the risk-free interest rate in the United States is $8 \%$ per annum, the risk-free interest rate in Japan is $5 \%$ per annum, and the volatility of the yen is $15 \%$ per annum. Calculate the delta, gamma, vega, theta, and rho of the financial institution's position. Interpret each number.

   A financial institution has just sold 1,000 7-month European call options on the Japanese yen. Suppose that the spot exchange rate is 0.80 cent per yen, the exercise price is 0.81 cent per yen, the risk-free interest rate in the United States is $8 \%$ per annum, the risk-free interest rate in Japan is $5 \%$ per annum, and the volatility of the yen is $15 \%$ per annum. Calculate the delta, gamma, vega, theta, and rho of the financial institution's position. Interpret each number.
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Options, Futures, and Other Derivatives
Options, Futures, and Other Derivatives
John C. Hull 10th Edition
Chapter 19, Problem 14 ↓

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Step 1

Delta measures the sensitivity of the option price to changes in the spot exchange rate. The delta of a call option is positive and ranges from 0 to 1. The delta can be calculated using the Black-Scholes formula: \[\Delta = e^{-rT}N(d_1)\] where: - \(r\) is the  Show more…

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A financial institution has just sold 1,000 7-month European call options on the Japanese yen. Suppose that the spot exchange rate is 0.80 cent per yen, the exercise price is 0.81 cent per yen, the risk-free interest rate in the United States is $8 \%$ per annum, the risk-free interest rate in Japan is $5 \%$ per annum, and the volatility of the yen is $15 \%$ per annum. Calculate the delta, gamma, vega, theta, and rho of the financial institution's position. Interpret each number.
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