By Yves Achdou

The former reviewer is totally improper in giving this ebook one big name. As a quant with a computational history, i've got came across this booklet to have first-class fabric.

**Read or Download Computational Methods for Option Pricing (Frontiers in Applied Mathematics) PDF**

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**Extra info for Computational Methods for Option Pricing (Frontiers in Applied Mathematics)**

**Example text**

7. European call by binomial tree. double binomial(const double SO) { double disc = exp(-r*dt); double u = (1+sqrt(exp(sigmap*sigmap*dt)-1))/disc; double d=(1-sqrt(exp(sigmap*sigmap*dt)-1))/disc, p = 0 . S[n] - K : 0 ; for(int m = M - l ; m > 0 ; m - - ) f o r ( i n t n=0; n

The proof is given in [90]. 25) and integrating in time between 0 and t. 11 applies for any European option with a payoff function in L 2 (R + ), in particular to vanilla puts. It does not apply to vanilla calls, and we will come back to this later. 24). Calling At the unbounded operator in L 2 (R+), it can be checked that for all / e [0, T] and for A. 10, the domain of At + A. 2. There exist a positive constant C and 0 < a. 24) belongs to D at any time t > 0, for any Cauchy data PQ € L 2 (R + ).

6 Complement: Binomial Trees The second most popular numerical method for pricing options is akin to Bellman's dynamic programming and uses a tree of possible events, the so-called binomial option pricing model. It leads to quite a good numerical method which is also easy to understand. , Sn = St, t = n8t) can evolve in only two ways: • either it goes up by a factor u > 1: Sn+i = uSn with probability p, or • it goes down by a factor d < 1: Sn+i = dSn with probability 1 — p. So if we denote by S™ one of the possible values of 5 at stage n, at the next stage we can have 18 Chapter 1.