Related papers: Implied Probabilities and Volatility in Credit Ris…

Contrary to the common view that exact pricing is prohibitive owing to the curse of dimensionality, this study proposes an efficient and unified method for pricing options under multivariate Black-Scholes-Merton (BSM) models, such as the…

We generalize Merton's asset valuation approach to systems of multiple financial firms where cross-ownership of equities and liabilities is present. The liabilities, which may include debts and derivatives, can be of differing seniority. We…

Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one,…

This study delves into the temporal dynamics within the equity market through the lens of bond traders. Recognizing that the riskless interest rate fluctuates over time, we leverage the Black-Derman-Toy model to trace its temporal…

We introduce a new method to calculate the credit exposure of European and path-dependent options. The proposed method is able to calculate accurate expected exposure and potential future exposure profiles under the risk-neutral and the…

We introduce a novel machine learning model for credit risk by combining tree-boosting with a latent spatio-temporal Gaussian process model accounting for frailty correlation. This allows for modeling non-linearities and interactions among…

In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims…

This paper investigates short-term behaviors of implied volatility of derivatives written on indexes in equity markets when the index processes are constructed by using a ranking procedure. Even in simple market settings where stock prices…

Risk assessment under different possible scenarios is a source of uncertainty that may lead to concerning financial losses. We address this issue, first, by adapting a robust framework to the class of spectral risk measures. Second, we…

Random-expiry options are nontraditional derivative contracts that may expire early based on a random event. We develop a methodology for pricing these options using a trinomial tree, where the middle path is interpreted as early expiry. We…

We propose a two-step framework for predicting the implied volatility surface over time without static arbitrage. In the first step, we select features to represent the surface and predict them over time. In the second step, we use the…

We investigate financial markets under model risk caused by uncertain volatilities. For this purpose we consider a financial market that features volatility uncertainty. To have a mathematical consistent framework we use the notion of…

Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true…

This paper considers the asset price p as relations C=pV between the value C and the volume V of the executed transactions and studies the consequences of this definition for the option pricing equations. We show that the classical BSM…

Existing approaches to asset-pricing under model-uncertainty adapt classical utility-maximization frameworks and seek theoretical comprehensiveness. We move toward practice by considering binary model-risks and by emphasizing 'constraints'…

Usually, in the Black-Scholes pricing theory the volatility is a positive real parameter. Here we explore what happens if it is allowed to be a complex number. The function for pricing a European option with a complex volatility has…

Pricing derivatives goes back to the acclaimed Black and Scholes model. However, such a modeling approach is known not to be able to reproduce some of the financial stylized facts, including the dynamics of volatility. In the mathematical…

We introduce a discrete binary tree for pricing contingent claims with the underlying security prices exhibiting history dependence characteristic of that induced by market microstructure phenomena. Example dependencies considered include…

Because the asset value of a private company does not observable except in quarterly reports, the structural model has not been developed for a private company. For this reason, this paper attempt to develop the Merton's structural model…

The use of cumulative incidence functions for characterizing the risk of one type of event in the presence of others has become increasingly popular over the past decade. The problems of modeling, estimation and inference have been treated…