Value -at-Risk on a portfolio of Options, Futures and Equities

1. Value-at-Risk on a portfolio of Options, Futures and Equities RadheshAgarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)

2. Calculating Value at Risk for Options, Futures and Equities

3. Monte Carlo Simulator The simulated prices are generated based on the Black-Scholes Terminal Price formula: St=S0*exp[(r – q - 0.5* σ ^2)t + σ tzt] Where: S0 is the spot price at time zero r is the risk free rate q is the dividend yield σ is the annualized volatility t is the duration since time zero Zt is a random sample from a normal distribution with μ = 0 & σ = 1.

4. Assumptions 1. Time step - 1 day Option Contract Expiry - 10 days Hence, 10 intermediate time steps taken 2. 100 scenarios Parameters S0 2000 r 0.15% q 0.01% σ 16.00% t 0.002739726 Terminal Price Scenario

5. Payoffs Payoff for a long futures = Terminal Price – Strike Payoff for a long call option = Maximum of (Terminal Price –Strike, 0) Payoff for the long put option = Maximum of (0, Strike-Terminal Price) Assumptions 1.Futures Contract, European Call and Put Option 2. Strike Price = 2020 Call Payoffs

6. Future Return Series Steps Discount each data point Simple average of prices for future dates

7. Output Worksheet Table • Observations • There is only a .27% chance that the worst case loss of over -23.34% • There is a 3.02% chance that loss will be over 11%

8. Call Option

9. Call Options • Observations • There is only a .27% chance that the worst case loss of over -14.34% • There is a 1.1% chance that loss will be over 5.24% At 95% confidence level the VaR is around 3%.

10. Put Option

11. Put Option • Observations • There is only a .27% chance that the worst case loss of over 3.83% • There is a 9.34% chance that loss will be over 1.29% This shows that at 95% confidence level the VaR is around 1.9%.

12. Sensitivity Analysis of VaR - Futures Observations Positive Correlation between volatility and High negative returns For medium volatility, the value at risk is at decent levels.

13. Sensitivity Analysis of VaR –Call Option Observations Positive Correlation between Value-at-Risk and Volatility For high volatility, though the confidence interval for positive return is on a lower side, the losses possible are generally low

14. Sensitivity Analysis of VaR – Put Option Observations At all 3 levels of volatility, VaR is similar Also, though the confidence interval for positive returns is on a lower side, the possible losses are not very high.

15. Thank you!