This program simulates delta hedging of European options in the Black-Scholes framework, with transaction costs and different rebalancing frequencies. Hedging more often reduces variance but increases transaction costs. The Option Type can be Call, Put, or Straddle. Sample output:
Option Parameters:
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Option Type: Straddle
Option Position: -1.0000
Initial Stock Price (S0): 100.0000
Strike Price (K): 100.0000
Time to Maturity (T): 1.0000
Risk-free Rate (r): 0.0000
Implied Volatility (sigma): 0.2500
Realized Volatility: 0.2000
Transaction Cost: 0.0010
Number of Simulations: 10000
Delta Hedging Simulation Results
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Rebalancing Mean Profit Std Dev Mean/Std
----------- ----------- ------- --------
0 4.1485 11.8594 0.3498
1 3.9619 12.0190 0.3296
4 3.8591 6.6110 0.5837
12 3.6983 4.1029 0.9014
52 3.4400 2.2811 1.5080
252 2.9649 1.3888 2.1349
504 2.5815 1.1150 2.3152
756 2.3201 0.9864 2.3520
1008 2.0844 0.8823 2.3625
2520 1.0321 0.4957 2.0820
Black-Scholes Price (Implied Volatility): 19.8953
Black-Scholes Price (Realized Volatility): 15.9311
BS Price Difference (Implied - Realized): 3.9642
Expected Profit (Ignoring T-Costs): 3.9642
Best Rebalancing Frequency (Max Mean/Std): 1008
Elapsed Time (s): 8.9850