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output.txt
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output.txt
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==================
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/
==================