Related papers: Implied Probabilities and Volatility in Credit Ris…
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…
Portfolio selection in the periodic investment of securities modeled by a multivariate Merton model with dependent jumps is considered. The optimization framework is designed to maximize expected terminal wealth when portfolio risk is…
We study specific nonlinear transformations of the Black-Scholes implied volatility to show remarkable properties of the volatility surface. Model-free bounds on the implied volatility skew are given. Pricing formulas for the European…
In structural credit risk models, default events and the ensuing losses are both derived from the asset values at maturity. Hence it is of utmost importance to choose a distribution for these asset values which is in accordance with…
We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be…
Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are studied. When volatility is time dependent, it is not reasonable to assume that…
Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and…
We propose a machine learning-based extension of the classical binomial option pricing model that incorporates key market microstructure effects. Traditional models assume frictionless markets, overlooking empirical features such as bid-ask…
We study markets with no riskless (safe) asset. We derive the corresponding Black-Scholes-Merton option pricing equations for markets where there are only risky assets which have the following price dynamics: (i) continuous diffusions; (ii)…
In this paper we study the short-time behavior of the at-the-money implied volatility for arithmetic Asian options with fixed strike price. The asset price is assumed to follow the Black-Scholes model with a general stochastic volatility…
In this letter, I consider the issue of pricing risky debt by following Merton's approach. I generalize Merton's results to the case where the interest rate is modeled by the CIR term structure. Exact closed forms are provided for the risky…
The vast majority of works on option pricing operate on the assumption of risk neutral valuation, and consequently focus on the expected value of option returns, and do not consider risk parameters, such as variance. We show that it is…
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 binomial tree method and the Monte Carlo (MC) method are popular methods for solving option pricing problems. However in both methods there is a trade-off between accuracy and speed of computation, both of which are important in…
We extend the classical Cox-Ross-Rubinstein binomial model in two ways. We first develop a binomial model with time-dependent parameters that equate all moments of the pricing tree increments with the corresponding moments of the increments…
The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic…
In this paper we study short-time behavior of the at-the-money implied volatility for Inverse European options with fixed strike price. The asset price is assumed to follow a general stochastic volatility process. Using techniques of the…
High precision analytical approximation is proposed for variance-covariance based risk allocation in a portfolio of risky assets. A general case of a single-period multi-factor Merton-type model with stochastic recovery is considered. The…
We investigate the quantification of demographic risk in a framework consistent with the market-consistent valuation imposed by Solvency II. We provide compact formulas for evaluating inflows and outflows of a portfolio of insurance…
In this paper, we developed the Merton's structural model for public companies under an assumption that liabilities of the companies are observed. Using Campbell and Shiller's approximation method, we obtain formulas of risk-neutral equity…