Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank...
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Transcript of Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank...
![Page 1: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/1.jpg)
Value-at-Risk on a portfolio of Options, Futures and Equities
Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)
![Page 2: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/2.jpg)
CALCULATING VALUE AT RISK FOR OPTIONS, FUTURES AND EQUITIES
![Page 3: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/3.jpg)
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.
![Page 4: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/4.jpg)
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
![Page 5: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/5.jpg)
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
![Page 6: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/6.jpg)
Future Return SeriesSteps1. Discount each data point2. Simple average of prices for future dates
![Page 7: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/7.jpg)
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%
![Page 8: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/8.jpg)
Call Option
![Page 9: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/9.jpg)
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%.
![Page 10: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/10.jpg)
Put Option
![Page 11: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/11.jpg)
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%.
![Page 12: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/12.jpg)
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.
![Page 13: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/13.jpg)
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
![Page 14: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/14.jpg)
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.
![Page 15: Value-at-Risk on a portfolio of Options, Futures and Equities Radhesh Agarwal (Ral13001) Shashank Agarwal (Sal13003) Sumit Jalan (Sjn13024)](https://reader036.fdocuments.in/reader036/viewer/2022062515/56649d1e5503460f949f1d59/html5/thumbnails/15.jpg)
Thank you!