Related papers: American Exchange option driven by a L\'evy proces…
In this paper we study the pricing of exchange options when underlying assets have stochastic volatility and stochastic correlation. An approximation using a closed-form approximation based on a Taylor expansion of the conditional price is…
We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility…
We study the barrier that gives the optimal time to exercise an American option written on a time-dependent Ornstein--Uhlenbeck process, a diffusion often adopted by practitioners to model commodity prices and interest rates. By framing the…
We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is…
This paper investigates analytic properties of American option prices under the finite moment log-stable (FMLS) model. Under this model the price of American options is characterised by the free boundary problem of a fractional partial…
Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range…
We study the regularity of the stochastic representation of the solution of a class of initial-boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal…
We consider the problem of finding a consistent upper price bound for exotic options whose payoff depends on the stock price at two different predetermined time points (e.g. Asian option), given a finite number of observed call prices for…
There exist several methods how more general options can be priced with call prices. In this article, we extend these results to cover a wider class of options and market models. In particular, we introduce a new pricing formula which can…
Options have provided a field of much study because of the complexity involved in pricing them. The Black-Scholes equations were developed to price options but they are only valid for European styled options. There is added complexity when…
We develop a practical framework for identifying and quantifying the hidden layers of risks and optionality embedded in American options by introducing stochasticity into one or more of their underlying determinants. The heuristic approach…
The Chicago Board Options Exchange Volatility Index (VIX) is calculated from SPX options and derivatives of VIX are also traded in market, which leads to the so-called ``consistent modeling" problem. This paper proposes a time-changed…
In this paper we develop an algorithm to calculate the prices and Greeks of barrier options in a hyper-exponential additive model with piecewise constant parameters. We obtain an explicit semi-analytical expression for the first-passage…
We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average…
This work focuses on the indifference pricing of American call option underlying a non-traded stock, which may be partially hedgeable by another traded stock. Under the exponential forward measure, the indifference price is formulated as a…
We develop a general method for derivative pricing. This approach has its roots in Shannon's Information Theory. The notion of $\lambda$-analyticity of L\'{e}vy models is introduced on the basis of which new representations of the pricing…
We develop an arbitrage-free random field LIBOR market model to price cross-currency derivatives. The uncertainty of the forward LIBOR rates of our cross-currency model is driven by a two time parameter random field instead of a finite…
One popular approach to option pricing in L\'evy models is through solving the related partial integro differential equation (PIDE). For the numerical solution of such equations powerful Galerkin methods have been put forward e.g. by Hilber…
We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating…
This study deals with the problem of pricing compound options when the underlying asset follows a mixed fractional Brownian motion with jumps. An analytic formula for compound options is derived under the risk neutral measure. Then, these…