数理金融
Siegel's paradox is a fundamental question in international finance about exchange rates for futures contracts and has puzzled many scholars for over forty years. The unorthodox approach presented in this article leads to an arbitrage-free…
Recently, the notion of cryptocurrencies has come to the fore of public interest. These assets that exist only in electronic form, with no underlying value, offer the owners some protection from tracking or seizure by government or…
In this paper we develop a framework for discretely compounding interest rates which is based on the forward price process approach. This approach has a number of advantages, in particular in the current market environment. Compared to the…
We propose an optimal portfolio problem in the incomplete market where the underlying assets depend on economic factors with delayed effects, such models can describe the short term forecasting and the interaction with time lag among…
In this work we study the optimal execution problem with multiplicative price impact in algorithm trading, when an agent holds an initial position of shares of a financial asset. The inter-selling-decision times are modelled by the arrival…
Option pricing is the most elemental challenge of mathematical finance. Knowledge of the prices of options at every strike is equivalent to knowing the entire pricing distribution for a security, as derivatives contingent on the security…
We introduce the concept of no-arbitrage in a credit risk market under ambiguity considering an intensity-based framework. We assume the default intensity is not exactly known but lies between an upper and lower bound. By means of the…
In this work we present an analytical model, based on the path-integral formalism of Statistical Mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under…
We introduce a price impact model which accounts for finite market depth, tightness and resilience. Its coupled bid- and ask-price dynamics induce convex liquidity costs. We provide existence of an optimal solution to the classical problem…
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 expected utility maximisation problem for exponential Levy models and HARA utilities in presence of illiquid asset in portfolio. This illiquid asset is modelled by an option of European type on another risky asset which is…
Empirical evidence suggests that fixed income markets exhibit unspanned stochastic volatility (USV), that is, that one cannot fully hedge volatility risk solely using a portfolio of bonds. While [1] showed that no two-factor…
The objective of this paper is to provide a comprehensive study no-arbitrage pricing of financial derivatives in the presence of funding costs, the counterparty credit risk and market frictions affecting the trading mechanism, such as…
We consider a dynamic market model of liquidity where unmatched buy and sell limit orders are stored in order books. The resulting net demand surface constitutes the sole input to the model. We prove that generically there is no arbitrage…
In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these…
We show that the moment explosion time in the rough Heston model [El Euch, Rosenbaum 2016, arxiv:1609.02108] is finite if and only if it is finite for the classical Heston model. Upper and lower bounds for the explosion time are…
We study a coin-tossing model used by a ratings agency to justify the sale of constant proportion debt obligations (CPDOs), and prove that it was impossible for CPDOs to achieve in a finite lifetime the Cash-In event of doubling its…
We investigate asymmetry of information in the context of robust approach to pricing and hedging of financial derivatives. We consider two agents, one who only observes the stock prices and another with some additional information, and…
We propose a fast and accurate numerical method for pricing European swaptions in multi-factor Gaussian term structure models. Our method can be used to accelerate the calibration of such models to the volatility surface. The pricing of an…
We introduce a new diffusion process Xt to describe asset prices within an economic bubble cycle. The main feature of the process, which differs from existing models, is the drift term where a mean-reversion is taken based on an exponential…