The square root constant elasticity of variance (CEV) process has been paid little attention in previous research on valuation of barrier options. In this paper we derive analytical option pricing formulae of up-and-out options with this process using the eigenfunction expansion technique. We develop an efficient algorithm to compute the eigenvalues where the basis functions in the formulae are...

One of the best examples of mathematically rigorous signal processing in finance is the Black-Scholes model for price evolution of financial options. To address the same problem, this paper proposes a Takagi-SugenoKang (TSK) fuzzy rule-based option pricing model that requires only a small number of rules to describe highly complex financial signals such as option prices. The findings for this d...

We study the convergence of at-the-money implied volatilities to the spot volatility in a general model with a Brownian component and a jump component of finite variation. This result is a consequence of the robustness of the Black–Scholes formula and of the central limit theorem for martingales.

This paper presents the contemporary Fundamental Theorem of Asset Pricing as being equivalent to approaches to pricing that emerged before 1700 in the context of Virtue Ethics. This is done by considering the history of science and mathematics in the thirteenth and seventeenth century. An explanation as to why these approaches to pricing were forgotten between 1700 and 2000 is given, along with...

This work provides an application of wavelet analysis to pricing and hedging path–dependent contingent claims within the framework of the Black–Scholes model.

The double barrier option is characterized by pay-off with strike K, maturity T, upper Su and lower Sd barrier levels and the corresponding rebates φu and φd which can be time dependent. We divide last four quantities by strike K and introduce new variables x = ln(S/K), xu = ln(Su/K), xd = ln(Sd/K). The value of European double barrier call option U(t, x) satisfies the extended Black-Scholes eq...