We develop a model for indifference pricing in derivatives markets where price quotes have bid-ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investors beliefs, risk preferences and financial position as well as on the price quotes. Computational techniques of convex optimisation allow for fast computation of the hedging portfolios and prices as well as sensitivities with respect to various model parameters. We illustrate the techniques by pricing and hedging of exotic derivatives on S&P index using call and put options, forward contracts and cash as the hedging instruments. The optimized static hedges provide good approximations of the options payouts and the spreads between indifference selling and buying prices are quite narrow as compared with the spread between super-and subhedging prices.

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This paper presents an explicit formula of conditional expectation for a product of polynomial functions and the discounted characteristic function based on the Cox–Ingersoll–Ross (CIR) process. We also propose an analytical formula as well as a very efficient and accurate approach, based on the finite integration method with shifted Chebyshev polynomial, to evaluate this expectation under the Extended CIR (ECIR) process. The formulas are derived by solving the equivalent partial differential equations obtained by utilizing the Feynman–Kac representation. In addition, we extend our results to derive an analytical formula of conditional expectation of a product of mixed polynomial functions and the discounted characteristic function. The accuracy and efficiency of the proposed scheme are also numerically shown for various modeling parameters by comparing them with those obtained from Monte Carlo simulations. In addition, to illustrate applications of the obtained formulas in finance, analytical pricing formulas for arrears and vanilla interest rate swaps under the ECIR process are derived. The pricing formulas become explicit under the CIR process. Finally, the fractional ECIR process is also studied as an extended case of our main results.

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This paper presents analytical formulas for pricing generalized swaps, including the moment swap, gamma swap, entropy swap and self-quantoed variance swap. The formulas are based on closed-form formulas for the conditional expectations of the product of the price and its logarithm and the product of the price and the convenience yield obtained by solving a partial differential equation corresponding to the infinitesimal generator for the two-dimensional diffusion process. In this respect, the formulas obtained are combinatorial in nature and are solved via an affine transformation involving the complete Bell polynomials. The formulas are quite suitable for practical usage with symmetric and skew-symmetric properties, i.e., they are simpler and more compact compared with those existing in the literature. Moreover, for moments swaps, we show in general that the strike price does not depend on the initial spot price but depends only on the initial convenience yield, which highlights the resulting versatility in this respect.