Related papers: Implied Probabilities and Volatility in Credit Ris…
In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the…
We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction…
We present a deep learning framework for pricing options based on market-implied volatility surfaces. Using end-of-day S\&P 500 index options quotes from 2018-2023, we construct arbitrage-free volatility surfaces and generate training data…
We explain the main concepts of Prospect Theory and Cumulative Prospect Theory within the framework of rational dynamic asset pricing theory. We derive option pricing formulas when asset returns are altered with a generalized Prospect…
This paper presents a method for incorporating risk aversion into existing decision tree models used in economic evaluations. The method involves applying a probability weighting function based on rank dependent utility theory to reduced…
Analytical, free of time consuming Monte Carlo simulations, framework for credit portfolio systematic risk metrics calculations is presented. Techniques are described that allow calculation of portfolio-level systematic risk measures…
The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…
We propose a method for extending a given asset pricing formula to account for two additional sources of risk: the risk associated with future changes in market--calibrated parameters and the remaining risk associated with idiosyncratic…
Motivated by the Corns-Satchell, continuous time, option pricing model, we develop a binary tree pricing model with underlying asset price dynamics following It\^o-Mckean skew Brownian motion. While the Corns-Satchell market model is…
We propose a modification of the classical Black-Derman-Toy (BDT) interest rate tree model, which includes the possibility of a jump with small probability at each step to a practically zero interest rate. The corresponding BDT algorithms…
One the one hand, rough volatility has been shown to provide a consistent framework to capture the properties of stock price dynamics both under the historical measure and for pricing purposes. On the other hand, market price of volatility…
This paper presents a convenient framework for modeling default process and pricing derivative securities involving credit risk. The framework provides an integrated view of credit valuation adjustment by linking distance-to-default,…
The problems of model and variable selections for classification trees are jointly considered. A penalized criterion is proposed which explicitly takes into account the number of variables, and a risk bound inequality is provided for the…
While defaults are rare events, losses can be substantial even for credit portfolios with a large number of contracts. Therefore, not only a good evaluation of the probability of default is crucial, but also the severity of losses needs to…
We analyse the behaviour of the implied volatility smile for options close to expiry in the exponential L\'evy class of asset price models with jumps. We introduce a new renormalisation of the strike variable with the property that the…
Classical asset pricing relies on the risk-neutral measure $Q$ for valuation, yet its economic interpretation is typically anchored in a physical measure $P$. This creates an inherent asymmetry: pricing is governed by $Q$, while meaning…
The aim of this paper is to compare two asset allocation methods for a pension scheme during the decumulation phase in the simplified portfolio selection between a risky asset following a geometric Brownian motion and a riskless asset. The…
Models to price long term loans in the securities lending business are developed. These longer horizon deals can be viewed as contracts with optionality embedded in them. This insight leads to the usage of established methods from…
We consider a stochastic volatility model with jumps where the underlying asset price is driven by the process sum of a 2-dimensional Brownian motion and a 2-dimensional compensated Poisson process. The market is incomplete, resulting in…
Option pricing in real markets faces fundamental challenges. The Black--Scholes--Merton (BSM) model assumes constant volatility and uses a linear generator $g(t,x,y,z)=-ry$, while lacking explicit behavioral factors, resulting in systematic…