In this paper we show that a Kelly trader is indifferent to trade derivative if and only the no-arbitrage price uniquely given by minimal martingale measure price, thus providing natural selection mechanism for option pricing in incomplete markets. We also unique indifference results market equilibrium sense no can improve magnitude of his instantaneous Sharpe ratio, trading derivative, actions...

The option pricing problem is one of central contents in modern finance. In this paper, European option pricing formula is formulated for Liu’s hybrid stock model with randomness and fuzziness. This formula may be regarded as a generalization of Black-Scholes formula and Qin-Li’s option pricing formula.

Traditional capital budgeting models cannot appropriately capture the value of IT-systems. Real Option Pricing Theory provides a useful economic perspective on the valuation of IT-systems, although no comprehensive review of the state of the art of real option pricing models for IT-investments has been published to date. This paper provides an overview of the applicability of real option theory...

Part I proposes a numeraire-invariant option pricing framework. It defines an option, its price process, and such notions as option indistinguishability and equivalence, domination, payoff process, trigger option, and semipositive option. It develops some of their basic properties, including price transitivity law, indistinguishability results, convergence results, and, in relation to nonnegati...

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...

This thesis examines the performance of five option pricing models with respect to the pricing of barrier options. The models include the Black-Scholes model and four stochastic volatility models ranging from the single-factor stochastic volatility model first proposed by Heston (1993) to a multi-factor stochastic volatility model with jumps in the spot price process. The stochastic volatility ...

Option pricing is a process to obtain the theoretical fair value of an option based on the factors affecting its price. Currently, the nonparametric and computational methods of option valuation are able to construct a model of the pricing formula from historical data. However, these models are generally based on a global learning paradigm, which may not be able to efficiently and accurately ca...

Real options modeling, which extends the ability of option pricing models to evaluate real assets, can be used to evaluate risky projects because of its capacity to handle uncertainties. This research utilizes possibility theory to represent private risks of a project, which are not reflected in the market and hence are not fully evaluated by standard option pricing models. Using a transformati...