Related papers: Scale-invariance and contingent claim pricing
This paper studies the pricing of contingent claims of American style, using indifference pricing by fully dynamic convex risk measures. We provide a general definition of risk-indifference prices for buyers and sellers in continuous time,…
We study auctions that are robust at any scale, i.e., they can be applied to sell both expensive and cheap items and achieve the best multiplicative approximations of the optimal revenue in the worst case. We show that the optimal mechanism…
We consider a stochastic volatility model where the dynamics of the volatility are given by a possibly infinite linear combination of the elements of the time extended signature of a Brownian motion. First, we show that the model is…
We derive a forward partial integro-differential equation for prices of call options in a model where the dynamics of the underlying asset under the pricing measure is described by a -possibly discontinuous- semimartingale. A uniqueness…
We study convexity and monotonicity properties of option prices in a model with jumps using the fact that these prices satisfy certain parabolic integro-differential equations. Conditions are provided under which preservation of convexity…
We consider conditional-mean hedging in a fractional Black-Scholes pricing model in the presence of proportional transaction costs. We develop an explicit formula for the conditional-mean hedging portfolio in terms of the recently…
A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for…
One of the fundamental questions in inflation is how to characterize the structure of different types of models in the field theoretic landscape. Proposals in this direction include attempts to directly characterize the formal structure of…
Realised pay-offs for discretisation-invariant swaps are those which satisfy a restricted `aggregation property' of Neuberger [2012] for twice continuously differentiable deterministic functions of a multivariate martingale. They are…
We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and studied such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with…
We consider the pricing of derivatives written on accumulated marks, such as weather derivatives or aggregate loss claims, using a self-exciting marked point process. The jump intensity mean-reverts between events and increases at jump…
We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…
This paper studies convex duality in optimal investment and contingent claim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions…
We consider that the price of a firm follows a non linear stochastic delay differential equation. We also assume that any claim value whose value depends on firm value and time follows a non linear stochastic delay differential equation.…
In this paper we derive robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating…
In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model…
We present empirical evidence on the relationship between demand shocks and price changes, conditional on returns to scale. We find that in industries with decreasing returns to scale, demand increases (which raise costs) correspond to…
Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…
We propose a constructive framework for the super-hedging problem of a European contingent claim under proportional transaction costs in discrete time. Our main contribution is an explicit recursive scheme that computes both the…
A standing assumption in the literature on proportional transaction costs is efficient friction. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation, as they usually appear in frictionless…