Historical simulation for the option example

Quantitative Risk Management in R

Alexander McNeil

Professor, University of York

Historical simulation

• Portfolio: single European call option on equity index
• Consider losses and profits over one day
• Changes to index value S, implied volatility $\sigma$ and interest rate r affect value of portfolio
• We consider S and $\sigma$ (and assume r stays constant)
• Create loss operator taking S and $\sigma$ as input and giving the loss or profit as output

Estimating VaR and ES

• Apply loss operator lossop() to historical log-returns of S&P 500 and VIX to get simulated losses
• Estimate VaR by sample quantile as before
• Estimate ES by average of losses exceeding VaR estimate

Let's practice!

Quantitative Risk Management in R