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Suppose that Monte Carlo simulation is being used to evaluate a European call option on
Chapter 21, Problem 21.16(choose chapter or problem)
Suppose that Monte Carlo simulation is being used to evaluate a European call option on a non-dividend-paying stock when the volatility is stochastic. How could the control variate and antithetic variable technique be used to improve numerical efficiency? Explain why it is necessary to calculate six values of the option in each simulation trial when both the control variate and the antithetic variable technique are used.
Questions & Answers
QUESTION:
Suppose that Monte Carlo simulation is being used to evaluate a European call option on a non-dividend-paying stock when the volatility is stochastic. How could the control variate and antithetic variable technique be used to improve numerical efficiency? Explain why it is necessary to calculate six values of the option in each simulation trial when both the control variate and the antithetic variable technique are used.
ANSWER:Step 1 of 3
The couple of sample sets from standardized normal distributions are required for the simulation. To generate variations in volatility, the first sample is required. Once the variations in volatility are known, the second sample is needed to generate variations in the stock price. By assuming constant volatility, the control variate technique involves working out a second simulation. To produce stock price variations similar to the first simulation, the same random number flow is used.