Related papers: Implied Probabilities and Volatility in Credit Ris…
In many insurance contexts, dependence between risks of a portfolio may arise from their frequencies. We investigate a dependent risk model in which we assume the vector of count variables to be a tree-structured Markov random field with…
In this paper is investigated the pricing problem of options on bonds with credit risk based on analysis on two kinds of solving problems for the Black-Scholes equations. First, a solution representation of the Black-Scholes equation with…
Volatility is a natural risk measure in finance as it quantifies the variation of stock prices. A frequently considered problem in mathematical finance is to forecast different estimates of volatility. What makes it promising to use deep…
We construct a statistical indicator for the detection of short-term asset price bubbles based on the information content of bid and ask market quotes for plain vanilla put and call options. Our construction makes use of the martingale…
We price and replicate a variety of claims written on the log price $X$ and quadratic variation $[X]$ of a risky asset, modeled as a positive semimartingale, subject to stochastic volatility and jumps. The pricing and hedging formulas do…
This article is the second one in a series on the use of scaling invariance in finance. In the first article (cond-mat/9906048), we introduced a new formalism for the pricing of derivative securities, which focusses on tradable objects…
We propose a new static parameterization of the implied volatility surface which is constructed by using polynomials of sigmoid functions combined with some other terms. This parameterization is flexible enough to fit market implied…
Risk management is an important practice in the banking industry. In this paper we develop a new methodology to estimate and predict the probability of default (PD) based on the rating transition matrices, which relates the rating…
In informationally efficient financial markets, option prices and this implied volatility should immediately be adjusted to new information that arrives along with a jump in underlying's return, whereas gradual changes in implied volatility…
Applications of the quantum algorithm for Monte Carlo simulation to pricing of financial derivatives have been discussed in previous papers. However, up to now, the pricing model discussed in such papers is Black-Scholes model, which is…
Value at risk (VaR) is a risk measure that has been widely implemented by financial institutions. This paper measures the correlation among asset price changes implied from VaR calculation. Empirical results using US and UK equity indexes…
Modern portfolio theory(MPT) addresses the problem of determining the optimum allocation of investment resources among a set of candidate assets. In the original mean-variance approach of Markowitz, volatility is taken as a proxy for risk,…
We develop two alternate approaches to arbitrage-free, market-complete, option pricing. The first approach requires no riskless asset. We develop the general framework for this approach and illustrate it with two specific examples. The…
We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial…
We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent…
The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a…
We provide closed-form market equilibrium formula consolidating informational imperfections and investors beliefs. Based on Merton's model, we characterize the equilibrium expected excess returns vector with incomplete information. We then…
In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error…
We study the risk premium impact in the Perturbative Black Scholes model. The Perturbative Black Scholes model, developed by Scotti, is a subjective volatility model based on the classical Black Scholes one, where the volatility used by the…
We propose a new model for the forecasting of both the implied volatility surfaces and the underlying asset price. In the spirit of Guyon and Lekeufack (2023) who are interested in the dependence of volatility indices (e.g. the VIX) on the…