This paper examines the out-of-sample performance of two common extensions of the Black-Scholes framework, namely a GARCH and a stochastic volatility option pricing model. The models are calibrated to intraday FTSE 100 option prices. We apply two sets of performance criteria, namely out-of-sample valuation errors and Value-at-Risk oriented measures. When we analyze the t to observed prices, GAR...

We reconsider the replication problem for contingent claims in a complete market under a general framework. Since there are various limitations in the Black–Scholes pricing formula, we propose a new method to obtain an explicit self–financing trading strategy expression for replications of claims in a general model. The main advantage of our method is that we propose using an orthogonal expansi...

In the original Black-Scholes model, the risk is quantified by a constant volatility parameter. It has been proposed by many authors that the volatilities should be modeled by a stochastic process to obtain a more realistic model. The volatility that corresponds to actual market data for option prices in Black-Scholes model is called the implied volatility. This volatility is in general depende...

In the Black-Scholes option price model Brownian motion and the underlying Normal distribution play a fundamental role. Empirical evidence however shows that the normal distribution is a very poor model to fit real-life data. In order to achieve a better fit we replace the Brownian motion by a special Lévy process: the Meixner process. We show that the underlying Meixner distribution allows an ...

The Black Scholes model of option pricing constitutes the cornerstone of contemporary valuation theory. However, the model presupposes the existence of several unrealistic assumptions including the lognormal distribution of stock market price processes. There, now, subsists abundant empirical evidence that this is not the case. Consequently, several generalisations of the basic model have been ...

denote an increment of the BM (with ds > 0). We also use N(μ, σ2) to denote a normal distribution with mean μ and variance σ2. Recall some of the key properties of BM: (i) B0 = 0; (ii) independent increments, i.e., dBs and dBt are independent, for any s + ds ≤ t; (iii) stationary increments, i.e., dBs follows a normal distribution N(0, ds). Note this last distribution depends only on the length...

In this paper, a new identification of the Lagrange multipliers by means of the Sumudu transform, is employed to  btain a quick and accurate solution to the fractional Black-Scholes equation with the initial condition for a European option pricing problem. Undoubtedly this model is the most well known model for pricing financial derivatives. The fractional derivatives is described in Caputo sen...

We consider a popular problem in finance, option pricing, through the lens of an online learning game between Nature and an Investor. In the Black-Scholes option pricing model from 1973, the Investor can continuously hedge the risk of an option by trading the underlying asset, assuming that the asset’s price fluctuates according to Geometric Brownian Motion (GBM). We consider a worst-case model...

– We show, by studying in detail the market prices of options on liquid markets, that the market has empirically corrected the simple, but inadequate Black-Scholes formula to account for two important statistical features of asset fluctuations: “fat tails” and correlations in the scale of fluctuations. These aspects, although not included in the pricing models, are very precisely reflected in t...

This article develops an option pricing model to evaluate knowledge management (KM) activities from the following perspectives: knowledge creation, knowledge conversion, knowledge circulation, and knowledge carry out. This paper makes three important contributions: (1) it provides a formal theoretical grounding for the validity of the Black-Scholes model that might be employed to KM; (2) it pro...