Page 6 of Page 7 of Comparing a basket put with 3 single v anilla puts. Page 8 of Premium sa ved as a function of correlation. Basket option v s. Page 9 of TV approximation in Blac k-Scholes with moment. A more accurate and equally fast approximation. Gentle appro ximation of the TV. Page 10 of Page 11 of Standard Momen t Matching.
Basket options should be priced in a consistent w ay with. Hence the basic model assumption is a log-normal pro-. A decomposition into uncorrelated components of the. The cov ariance matrix is given b y. Page 12 of F ollowing [ 7 ] and [ 8 ], a simple approximation method. Page 13 of W e solve these equations for the drift and v olatility.
Page 14 of In these formulas w e now use the moments for the bask et. TV via Black-Sc holes-Merton formula for plain v anilla. Here N denotes the cumulativ e normal distribution. Page 15 of F or details see [ 6 ]. Page 16 of Gen tle Approximation of the TV. W e follow [ 4 ], include foreign interest rates, generalize.
The v alue function takes the form of the Black-Sc holes. Page 17 of Page 18 of The deltas can be obtained based on homogeneity meth-. Page 19 of Deriv ation of the V alue F unction. Page 20 of T is now a w eighted arithmethic av erage of. Hence we expect to obtain a decent appro ximation at. Page 21 of More precisely we do the v aluation as follows. Page 22 of Page 23 of T is n -v ariate normal.
Then its moment gener-. This allows in particular to compute the expectation. Page 24 of Optimal Strik e Decomp osition.
Page 25 of W e call the sum of the calls a naive b asket call with. The v alue of the actual basket option corresponding to. Page 26 of This minimization can be done as follows. Page 27 of This system does not seem to have a closed-form solu-.
The problem boils down. The practical implementation of this result requires. It means to determine the zero of. Page 28 of In markets whose underlyings ha ve. Page 29 of The arrows mark the mar-. Page 30 of This method also allows hedging correlation risk by. Page 31 of W eighted Mon te Carlo assigns probabilities to each ex-. These paths and assigned. The W eighted Mon te Carlo Engine. Page 32 of The W eighted Monte Carlo Engine. W e follow Av ellaneda et al.
Page 33 of Page 34 of Page 35 of Ho w to Find the Probabilities. Kul lb ack-Leibler r elative entr opy. Page 36 of Dual F ormulation of the Constrain t Mini-. Page 37 of W e know the gradien t. Therefore, we can use the fast gradien t-based optimiza-. Page 38 of Howev er, this makes the implemen-. Included a term structure of for-. Only with the forwards, the put-call-parity. Page 39 of Mark et, Contract and Numerical Constan ts.
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