Pricing of Securities
We consider the problem of exponential utility indifference valuation under the simplified framework where traded and nontraded assets are uncorrelated but where the claim to be priced possibly depends on both. Traded asset prices follow a…
We develop a model for the dynamic evolution of default-free and defaultable interest rates in a LIBOR framework. Utilizing the class of affine processes, this model produces positive LIBOR rates and spreads, while the dynamics are…
We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential L\'evy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time…
We consider the pricing and hedging of exotic options in a model-independent set-up using \emph{shortfall risk and quantiles}. We assume that the marginal distributions at certain times are given. This is tantamount to calibrating the model…
We study the pricing problem for corporate defaultable bond from the viewpoint of the investors outside the firm that could not exactly know about the information of the firm. We consider the problem for pricing of corporate defaultable…
We compute the value of a variance swap when the underlying is modeled as a Markov process time changed by a L\'{e}vy subordinator. In this framework, the underlying may exhibit jumps with a state-dependent L\'{e}vy measure, local…
This paper considers general term structure models like the ones appearing in portfolio credit risk modelling or life insurance. We give a general model starting from families of forward rates driven by infinitely many Brownian motions and…
The research presented in this work is motivated by some recent papers regarding hedging and valuation of financial securities subject to funding costs, collateralization and counterparty credit risk. Our goal is to provide a sound…
G-framework is presented by Peng [41] for measure risk under uncertainty. In this paper, we define fractional G-Brownian motion (fGBm). Fractional G-Brownian motion is a centered G-Gaussian process with zero mean and stationary increments…
It is well-known that the Black-Scholes formula has been derived under the assumption of constant volatility in stocks. In spite of evidence that this parameter is not constant, this formula is widely used by financial markets. This paper…
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…
The possibility of statistical evaluation of the market completeness and incompleteness is investigated for continuous time diffusion stock market models. It is known that the market completeness is not a robust property: small random…
We obtain an explicit formula for the bilateral counterparty valuation adjustment of a credit default swaps portfolio referencing an asymptotically large number of entities. We perform the analysis under a doubly stochastic intensity…
An efficient method to price bonds with optional sinking feature is presented. Such instruments equip their issuer with the option (but not the obligation) to redeem parts of the notional prior to maturity, therefore the future cash flows…
In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains…
In this paper, we consider a discrete time economy where we assume that the short term interest rate follows a quadratic term structure of a regime switching asset process. The possible non-linear structure and the fact that the interest…
This paper is concerned with the following Markovian stochastic differential equation of mean-reversion type \[ dR_t= (\theta +\sigma \alpha(R_t, t))R_t dt +\sigma R_t dB_t \] with an initial value $R_0=r_0\in\mathbb{R}$, where…
In this paper we present a very simple way to price a class of barrier options when the underlying process is driven by a huge class of L\'evy processes. To achieve our goal we assume that our market satisfies a symmetry property. In case…
In this note we show how to replicate a stylized CDS with a repurchase agreement and an asset swap. The latter must be designed in such a way that, on default of the issuer, it is terminated with a zero close-out amount. This break clause…
Hedging strategies in bond markets are computed by martingale representation and the Clark-Ocone formula under the choice of a suitable of numeraire, in a model driven by the dynamics of bond prices. Applications are given to the hedging of…