Related papers: On American VIX options under the generalized 3/2 …
We apply vector quantisation within mixed one- and two-factor Bergomi models to implement a fast and efficient approach for option pricing in these models. This allows us to calibrate such models to market data of VIX futures and options.…
In this paper we derive an easily computed approximation to European basket call prices for a local volatility jump-diffusion model. We apply the asymptotic expansion method to find the approximate value of the lower bound of European…
We continue a series of papers devoted to construction of semi-analytic solutions for barrier options. These options are written on underlying following some simple one-factor diffusion model, but all the parameters of the model as well as…
In financial markets, accurately measuring the risk of future fluctuations in asset prices is of paramount importance. Studies such as Carr and Madan have shown that the expected value of the quadratic variation of log prices can be…
It is well known that in models with time-homogeneous local volatility functions and constant interest and dividend rates, the European Put prices are transformed into European Call prices by the simultaneous exchanges of the interest and…
In this paper we provide a theoretical analysis of Variable Annuities with a focus on the holder's right to an early termination of the contract. We obtain a rigorous pricing formula and the optimal exercise boundary for the surrender…
The CEV model subsumes some of the previous option pricing models. An important parameter in the model is the parameter b, the elasticity of volatility. For b=0, b=-1/2, and b=-1 the CEV model reduces respectively to the BSM model, the…
We consider as given a discrete time financial market with a risky asset and options written on that asset and determine both the sub- and super-hedging prices of an American option in the model independent framework of ArXiv:1305.6008. We…
In stochastic Volterra rough volatility models, the volatility follows a truncated Brownian semi-stationary process with stochastic vol-of-vol. Recently, efficient VIX pricing Monte Carlo methods have been proposed for the case where the…
In equity and foreign exchange markets the risk-neutral dynamics of the underlying asset are commonly represented by stochastic volatility models with jumps. In this paper we consider a dense subclass of such models and develop analytically…
This work examines a stochastic volatility model with double-exponential jumps in the context of option pricing. The model has been considered in previous research articles, but no thorough analysis has been conducted to study its quality…
We consider call option prices in diffusion models close to expiry, in an asymptotic regime ("moderately out of the money") that interpolates between the well-studied cases of at-the-money options and out-of-the-money fixed-strike options.…
When trading American and Asian options in the FX derivatives market, banks must calculate prices using a complex mathematical model. It is often observed that different models produce varying prices for the same exotic option, which…
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 consider optimal control of an elliptic two-point boundary value problem governed by functions of bounded variation (BV). The cost functional is composed of a tracking term for the state and the BV-seminorm of the control. We use the…
In this paper, we introduce a data-driven, single-parameter Markov diffusion model for the VIX. The volatility factor evolves in $(-1,1)$ with a uniform invariant distribution ensured by Legendre polynomials, mapped to the empirical…
In this paper we consider the following optimal stopping problem $$V^{\omega}_{\rm A}(s) = \sup_{\tau\in\mathcal{T}} \mathbb{E}_{s}[e^{-\int_0^\tau \omega(S_w) dw} g(S_\tau)],$$ where the process $S_t$ is a jump-diffusion process,…
In this paper we study a general framework of American put option with stochastic volatility whose value function is associated with a 2-dimensional parabolic variational inequality with degenerate boundaries. We apply PDE methods to…
Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the…
According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price-dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations…