Determine the efficiency of finite differences
Determine the efficiency of finite differences?
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Finite differences are extremely good at coping with low dimensions, and that are the method of choice when you have a contract with embedded decisions. They are excellent for non-linear differential equations.
The time taken to price an option and compute the sensitivities to underlying(s) and time using the explicit finite-difference method will be
O(M ε-1-d/2),
Here M is the no. of different options in the portfolio and we need an accuracy of ε, and d is the no. of dimensions except time. So when we have a non-path-dependent option upon a single underlying so d = 1. Note there that we may require one piece of code per option, therefore M in the above.
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The discussion of zero-coupon bonds in the text gave an instance of two zero-coupon bonds issued through Commerzbank. The DM300, 000,000 issues due in the year of 1995 sold at 50 percent of face value and the DM300, 000,000 due in the year of 2000 sold a
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