Related papers: Risk Neutral Option Pricing With Neither Dynamic H…
We consider a portfolio with call option and the corresponding underlying asset under the standard assumption that stock-market price represents a random variable with lognormal distribution. Minimizing the variance (hedging risk) of the…
The approach that allows find European option price on the assumption of hedging at discrete times is proposed. The routine allows find the option price not for lognormal distribution functions of underlying asset only but for wide enough…
We investigate the relation between the fair price for European-style vanilla options and the distribution of short-term returns on the underlying asset ignoring transaction and other costs. We compute the risk-neutral probability density…
Following the foundational work of the Black--Scholes model, extensive research has been developed to price the option by addressing its underlying assumptions and associated pricing biases. This study introduces a novel framework for…
We develop two alternate approaches to arbitrage-free, market-complete, option pricing. The first approach requires no riskless asset. We develop the general framework for this approach and illustrate it with two specific examples. The…
We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…
A new method is proposed to obtain the risk neutral probability of share prices without stochastic calculus and price modeling, via an embedding of the price return modeling problem in Le Cam's statistical experiments framework.…
The price of a stock will rarely follow the assumed model and a curious investor or a Regulatory Authority may wish to obtain a probability model the prices support. A risk neutral probability ${\cal P}^*$ for the stock's price at time $T$…
In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the…
The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the…
The vast majority of works on option pricing operate on the assumption of risk neutral valuation, and consequently focus on the expected value of option returns, and do not consider risk parameters, such as variance. We show that it is…
The paper summarizes key results of the benchmark approach with a focus on the concept of benchmark-neutral pricing. It applies these results to the pricing of an extreme-maturity European put option on a well-diversified stock index. The…
A version of indifference valuation of a European call option is proposed that includes statistical regularities of nonstochastic randomness. Classical relations (forward contract value and Black-Scholes formula) are obtained as particular…
We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European,…
We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time tau. This is accomplished by assuming that the underlying noise in the system is…
We describe the pricing and hedging of financial options without the use of probability using rough paths. By encoding the volatility of assets in an enhancement of the price trajectory, we give a pathwise presentation of the replication of…
In this paper the valuation problem of a European call option in presence of both stochastic volatility and transaction costs is considered. In the limit of small transaction costs and fast mean reversion, an asymptotic expression for the…
We reconsider the problem of option pricing using historical probability distributions. We first discuss how the risk-minimisation scheme proposed recently is an adequate starting point under the realistic assumption that price increments…
This article considers the pricing and hedging of a call option when liquidity matters, that is, either for a large nominal or for an illiquid underlying asset. In practice, as opposed to the classical assumptions of a price-taking agent in…
The Black-Scholes model (sometimes known as the Black-Scholes-Merton model) gives a theoretical estimate for the price of European options. The price evolution under this model is described by the Black-Scholes formula, one of the most…