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Riding on a Smile
This paper studies the hedging of derivatives whose pricing formulas are periodically recalibrated in the presence of model risk. We assume that the price and implied parameter processes are observed in the market but the true model of these processes is unknown. Given multiple candidates for the true model, we define a model set of candidates for the true model. We study the minimum hedging error and an optimal strategy under the worst situation and show the procedure for their calculation. Furthermore some numerical examples are provided to illustrate the impact of model risk on the optimal hedging.
We use an artificial neural network for finance in two directions: to estimate prices and Greeks based on the geometric Brownian motion and the constant elasticity of variance model for European options, and to construct a local volatility surface. To show the efficiency and successful usage of the network, we compare prices and Greeks obtained by a solution formula and by the artificial neural network when there is a solution formula is known. Then, we calculate Dupire’s equations to construct a local volatility surface by the network.
In this manuscript, we introduced the radial basis function based three implicit-explicit (IMEX) finite difference techniques for pricing European and American options in an extended Markovian regime-switching jump-diffusion (RSJD) economy. A partial integrodifferential equation (PIDE) yields the values of the European option, which is one of the financial options, and a linear complementary problem (LCP) yields the prices of the American option. To solve the LCP for American option pricing, we combine the suggested techniques with the operator splitting methods. The suggested methods are designed to prevent the use of any fixed-point repetition approaches at each economic stage and time increment. We analyzed the stability of the proposed time discretization methods. We performed numerical experiments and illustrated the second-order convergence and efficiency of the three IMEX numerical techniques (BDF2, CNAB, CNLF) under the extended RSJD model.
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