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diff --git a/output.txt b/output.txt new file mode 100644 index 0000000..b3739b0 --- /dev/null +++ b/output.txt @@ -0,0 +1,71 @@ +================== +Pricing Asian options +================== +(i) = 1.4101 +- 0.0569 with 10000 trials +(i) = 1.4339 +- 0.0191 with 100000 trials +(i) = 1.4292 +- 0.0060 with 1000000 trials +================== +(ii) = 1.4344 +- 0.0381 with 10000 trials +(ii) = 1.3561 +- 0.0114 with 100000 trials +(ii) = 1.3582 +- 0.0036 with 1000000 trials +================== +(iii) = 1.3944 +- 0.1291 with 10000 trials +(iii) = 1.4562 +- 0.0388 with 100000 trials +(iii) = 1.4790 +- 0.0124 with 1000000 trials +================== +How do the prices compare? +We see that Asian options with more frequent setting dates are more expensive. +This is because the averaging is less pronounced with more setting dates, +making the Asian option more volatile. +================== +(vanilla) = 3.5564 +- 0.0471 with 10000 trials +(vanilla) = 3.5470 +- 0.0148 with 100000 trials +(vanilla) = 3.5491 +- 0.0047 with 1000000 trials +================== +How do the prices compare with a vanilla option? +We see that Asian options are cheaper than vanilla options. +This is because Asian options are less volatile, due to the averaging feature - +the volatility of the averaged price is less volatile than the spot price. +================== +How does the speed of convergence vary? +The rate of convergence is faster for sparser date settings, as seen by the +standard error. More dense date settings converge slower as the timing +evolution needs to be simulated. For the same reason, vanilla options converge +the fastest. +================== +Pricing discrete barrier options +================== +(i) = 3.5064 +- 0.1214 with 10000 trials +(i) = 3.5232 +- 0.0376 with 100000 trials +(i) = 3.5354 +- 0.0119 with 1000000 trials +================== +(ii) = 0.0028 +- 0.0025 with 10000 trials +(ii) = 0.0021 +- 0.0007 with 100000 trials +(ii) = 0.0017 +- 0.0002 with 1000000 trials +================== +(iii) = 4.3125 +- 0.0856 with 10000 trials +(iii) = 4.1930 +- 0.0282 with 100000 trials +(iii) = 4.2188 +- 0.0089 with 1000000 trials +================== +(iv) = 0.0000 +- 0.0000 with 10000 trials +(iv) = 0.0000 +- 0.0000 with 100000 trials +(iv) = 0.0000 +- 0.0000 with 1000000 trials +================== +(vanilla call) = 3.5461 +- 0.0469 with 10000 trials +(vanilla call) = 3.5543 +- 0.0148 with 100000 trials +(vanilla call) = 3.5452 +- 0.0047 with 1000000 trials +================== +(vanilla put) = 4.5581 +- 0.0381 with 10000 trials +(vanilla put) = 4.5026 +- 0.0118 with 100000 trials +(vanilla put) = 4.5036 +- 0.0037 with 1000000 trials +================== +Compare prices and speed of convergence. Also compare prices with +the vanilla option. +Similar to Asian options, the rate of convergence is faster for sparser date +settings. Vanilla options converge the fastest. +Discrete barrier options can be much cheaper than vanilla options. This is +because these type of options offer less flexibility compared to vanilla +options, and thus this is priced in. +================== +Shivesh Mandalia https://shivesh.org/ +================== |