value-at-risk on a portfolio of options, futures and equities radhesh agarwal (ral13001) shashank...

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

Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)

CALCULATING VALUE AT RISK FOR OPTIONS, FUTURES AND EQUITIES

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.

Terminal Price Scenario

Assumptions1. Time step - 1 dayOption Contract Expiry - 10 daysHence,10 intermediate time steps taken2. 100 scenarios

Parameters S0 2000 r 0.15% q 0.01% σ 16.00% t 0.002739726

Payoffs Assumptions1.Futures Contract,European Call and Put Option2. Strike Price = 2020

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)

Call Payoffs

Future Return SeriesSteps1. Discount each data point2. Simple average of prices for future dates

Output Worksheet TableObservations 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%

Call Option

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%.

Put Option

Put OptionObservations 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%.

Sensitivity Analysis of VaR - Futures

Observations

1. Positive Correlation between volatility and High negative returns

2. For medium volatility, the value at risk is at decent levels.

Sensitivity Analysis of VaR –Call Option

Observations

1. Positive Correlation between Value-at-Risk and Volatility

2. For high volatility, though the confidence interval for positive return is on a lower side, the losses possible are generally low

Sensitivity Analysis of VaR – Put Option

Observations

1. At all 3 levels of volatility, VaR is similar

2. Also, though the confidence interval for positive returns is on a lower side, the possible losses are not very high.

Thank you!