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Stochastic dividend discount models (Hurley and Johnson, 1994 and 1998, Yao, 1997) present expressions for the expected value of stock prices when future dividends evolve according to some random scheme. In this paper we try to offer a more…
A three-dimensional extension of the structural default model with firms' values driven by correlated diffusion processes is presented. Green's function based semi-analytical methods for solving the forward calibration problem and backward…
In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…
Classical solvable stochastic volatility models (SVM) use a CEV process for instantaneous variance where the CEV parameter $\gamma$ takes just few values: 0 - the Ornstein-Uhlenbeck process, 1/2 - the Heston (or square root) process, 1-…
In this paper we propose a novel pricing-hedging framework for volatility derivatives which simultaneously takes into account rough volatility and volatility jumps. Our model directly targets the instantaneous variance of a risky asset and…
This paper discusses models of inflation based on global supersymmetry. It is shown that there are parameter ranges, consisent with observational constraints, for which warm inflation occurs and supergravity effects can be neglected. There…
We derive analytic formulae which link $\alpha$, $\nu$ and $\rho$ parameters in Andreasen-Huge style SABR model to the ATM price and option prices at four strikes close to ATM. Based on these formulae we give a characterisation for the SABR…
In this paper, we relax the power parameter of instantaneous variance and develop a new stochastic volatility plus jumps model that generalize the Heston model and 3/2 model as special cases. This model has two distinctive features. First,…
The impact of trades on asset prices is a crucial aspect of market dynamics for academics, regulators and practitioners alike. Recently, universal and highly nonlinear master curves were observed for price impacts aggregated on all…
In this paper we extend discrete time semi-static trading strategies by also allowing for dynamic trading in a finite amount of options, and we study the consequences for the model-independent super-replication prices of exotic derivatives.…
In this paper we show how to approximate a Heath-Jarrow-Morton dynamics for the forward prices in commodity markets with arbitrage-free models which have a finite dimensional state space. Moreover, we recover a closed form representation of…
We present a simple hybrid dynamical model as a tool to investigate behavioral strategies based on trend following. The multiplicative symbolic dynamics are generated using a lognormal diffusion model for the at-the-money implied volatility…
The paper proposes a class of financial market models which are based on inhomogeneous telegraph processes and jump diffusions with alternating volatilities. It is assumed that the jumps occur when the tendencies and volatilities are…
We apply Geometric Arbitrage Theory to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. We obtain closed form equations involving default intensities and…
We estimate prices of exotic options in a discrete-time model-free setting when the trader has access to market prices of a rich enough class of exotic and vanilla options. This is achieved by estimating an unobservable quantity called…
We obtain new closed-form pricing formulas for contingent claims when the asset follows a Dupire-type local volatility model. To obtain the formulas we use the Dyson-Taylor commutator method that we have recently developed in [5, 6, 8] for…
We consider the problem of finding model-independent bounds on the price of an Asian option, when the call prices at the maturity date of the option are known. Our methods differ from most approaches to model-independent pricing in that we…
We design three continuous--time models in finite horizon of a commodity price, whose dynamics can be affected by the actions of a representative risk--neutral producer and a representative risk--neutral trader. Depending on the model, the…
This article proposes a calibration framework for complex option pricing models that jointly fits market option prices and the term structure of variance. Calibrated models under the conventional objective function, the sum of squared…
This article is a sequel to [A.H.M.P]. In [A.H.M.P], we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic delay equation with fixed delays in the drift and diffusion…