Related papers: On the Perpetual American Put Options for Level De…
This paper presents a derivation of the explicit price for the perpetual American put option time-capped by the first drawdown epoch beyond a predefined level. We consider the market in which an asset price is described by geometric L\'evy…
We study the behavior of the critical price of an American put option near maturity in the Jump diffusion model when the underlying stock pays dividends at a continuous rate and the limit of the critical price is smaller than the stock…
We analyse the behaviour of the implied volatility smile for options close to expiry in the exponential L\'evy class of asset price models with jumps. We introduce a new renormalisation of the strike variable with the property that the…
In this paper, we develop a 4/2 stochastic volatility plus jumps model, namely, a new stochastic volatility model including the Heston model and 3/2 model as special cases. Our model is highly tractable by applying the Lie symmetries theory…
In the present paper we present a finite element approach for option pricing in the framework of a well-known stochastic volatility model with jumps, the Bates model. In this model the asset log-returns are assumed to follow a…
We study the behavior of the critical price of an American put option near maturity in the exponential L\'evy model when the underlying stock pays dividends at a continuous rate. In particular, we prove that, in situations where the limit…
We regard options on VIX and Realised Variance as solutions to path-dependent partial differential equations (PDEs) in a continuous stochastic volatility model. The modeling assumption specifies that the instantaneous variance is a $C^3$…
Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options:…
We analyze and calculate the early exercise boundary for a class of stationary generalized Black-Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the…
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…
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…
In this article, we consider a risky asset $X$ for which evolution follows a model proposed by D.G. Hobson and L.C.G. Rogers\cite{HR98}. We assume that the volatility of $X$ depends on the ratio of the present value and the exponentially…
We give an analytical characterization of the price function of an American option in Heston-type models. Our approach is based on variational inequalities and extends recent results of Daskalopoulos and Feehan (2011). We study the…
In this paper, we investigate the generalization of the Call-Put duality equality obtained in [1] for perpetual American options when the Call-Put payoff $(y-x)^+$ is replaced by $\phi(x,y)$. It turns out that the duality still holds under…
We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price $\pi$ is given…
We study the problem of option replication under constant proportional transaction costs in models where stochastic volatility and jumps are combined to capture the market's important features. Assuming some mild condition on the jump size…
American options are financial instruments that can be exercised at any time before expiration. In this paper we study the problem of pricing this kind of derivatives within a framework in which some of the properties --volatility and…
In this paper we examine the problem of valuing an exotic derivative known as the American passport option where the underlying is driven by a L\'evy process. The passport option is a call option on a trading account. We derive the pricing…
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…
In this paper, we present a novel approach to solving the American put options pricing model by hugely relying on a front-fixing Crank-Nicolson finite difference method. Since the American put option pricing model is a widely used financial…