Elements of Financial Risk Management
Focusing on implementation, this book is for practitioners in the financial services and investment industries, as well as graduate students and advanced undergraduates who want exposure to these techniques.
TABLE OF CONTENTS Elements of Financial Risk Management
6.10. EMPIRICAL EXERCISES ON CD-ROM
6.10. EMPIRICAL EXERCISES ON CD-ROM
Open the Chapter6Data.xls file from the CD-ROM. The file contains European call options on the S&P 500 from August 29, 2002.
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Calculate the BSM price for each option using a standard deviation of 0.015 per day. Using Solver, find the volatility that minimizes the mean squared pricing error using 0.015 as a starting value. Keep the BSM prices that correspond to this optimal volatility and use these prices below.
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Scatter plot the BSM pricing errors (actual price less model price) against moneyness defined as (S/X) for the different maturities.
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Calculate the implied BSM volatility (standard deviation) for each of the options. You can use Excel s Solver to do this. Scatter plot the implied volatilities against moneyness.
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Fit the Gram-Charlier option price to the data. Estimate a model with skewness only. Use nonlinear least squares (NLS) again.
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Regress implied volatility on a constant, moneyness, the time-to-maturity divided by 365, each variable squared, and their cross product. Calculate the fitted BSM volatility from the regression for each option. Calculate the ad hoc IVF price for each option using the fitted values for volatility.
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Redo the IVF estimation using NLS to minimize the mean squared pricing error (MSE). Call this MIVF. Use the IVF regression coefficients as starting values.
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Calculate the square root of the mean squared pricing error from the IVF and MIVF models and compare them to the square root of the MSE from the standard BSM model and...
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