I am struggling with this new concept of Monte Carlo Simulation based option valuation.
For testing I want to price options on a stock which follows GBM. For illustration, I have considered 2 time steps and 3 paths.
Time1: 12, 14, 13
Time2: 17, 14, 10
So, average price for valuation period is: average(12, 14, 13, 17, 14, 10) = 13.33
Avg for Time1 is: average(12, 14, 13) = 13
Avg for Time2 is: average(17, 14, 10) = 13.67
Assuming strike for call options which needs to be valued is 13.5
Hence, intrinsic value:
Time1 is: max(13 - 13.33, 0) = 0
Time2 is: max(13.67 - 13.00, 0) = 0.67
For option total value,
Time1: average(max(12 - 13.5, 0), max(14 - 13.5, 0), max(13 - 13.5, 0 )) = 0.167
Time2: average(max(17 - 13.5, 0), max(14 - 13.5, 0), max(10 - 13.5, 0 )) = 1.33
Hence, option extrinsic value is total value minus intrinsic value:
Time1: 0.167 - 0 = 0.167
Time2 = 1.33 - 0.67 = 0.96
Am I right in my understanding ?
For testing I want to price options on a stock which follows GBM. For illustration, I have considered 2 time steps and 3 paths.
Time1: 12, 14, 13
Time2: 17, 14, 10
So, average price for valuation period is: average(12, 14, 13, 17, 14, 10) = 13.33
Avg for Time1 is: average(12, 14, 13) = 13
Avg for Time2 is: average(17, 14, 10) = 13.67
Assuming strike for call options which needs to be valued is 13.5
Hence, intrinsic value:
Time1 is: max(13 - 13.33, 0) = 0
Time2 is: max(13.67 - 13.00, 0) = 0.67
For option total value,
Time1: average(max(12 - 13.5, 0), max(14 - 13.5, 0), max(13 - 13.5, 0 )) = 0.167
Time2: average(max(17 - 13.5, 0), max(14 - 13.5, 0), max(10 - 13.5, 0 )) = 1.33
Hence, option extrinsic value is total value minus intrinsic value:
Time1: 0.167 - 0 = 0.167
Time2 = 1.33 - 0.67 = 0.96
Am I right in my understanding ?
