arXiv research

Optimizes risk-neutral probabilities for derivative pricing.

The paper shows how to calculate risk-neutral default probabilities from bid and ask CDS quotes.

Proposes a method to construct risk-neutral marginals from arbitrage-free option prices.

Project estimates risk-neutral dependence from option prices.

Develops a binary tree model for option pricing with skew dynamics.

The risk-neutral option pricing method under GARCH intensity model is examined. The GARCH intensity model incorporates the characteristics of financial return series such as volatility clustering, leverage effect and conditional asymmetry. The GARCH intensity option pricing model has flexibility in changing the volatil…

Developed Merton's model for public companies using observed liabilities.

Paper derives Thiele's equation for unit-linked policies in a stochastic volatility model.

Study analyzes bond traders' views on equity market dynamics.

Two new methods for option pricing without or with a riskless asset.

Reflected geometric Brownian motion models are not arbitrage-free.

We investigate the existence of affine realizations for Lévy driven interest rate term structure models under the real-world probability measure, which so far has only been studied under an assumed risk-neutral probability measure. For models driven by Wiener processes, all results obtained under the risk-neutral appro…

Paper introduces benchmark-neutral pricing for long-term contracts.

Unified kernel for prediction markets reduces belief variance forecast error.

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, under any general probability distribution, bypassing the Black-Scholes-Merton …

New formula for portfolio risk management using conditional PDEs.

This note explores the mathematical theory to solve modern gamblers ruin problems. We establish a ruin framework and solve for the probability of bankruptcy. We also show how this relates to the expected time to bankruptcy and review the risk neutral probabilities associated an adjustment to asymmetrical views.

New method recovers BSDE from financial data without ergodicity.

This paper proposes a new geometric framework for asset pricing.

In this paper we consider the pricing of variable annuities (VAs) with guaranteed minimum withdrawal benefits. We consider two pricing approaches, the classical risk-neutral approach and the benchmark approach, and we examine the associated static and optimal behaviors of both the investor and insurer. The first model …

The paper reviews historical and modern approaches to asset pricing probability measures.

This paper provides a methodology for fast and accurate pricing of the long-dated contracts that arise as the building blocks of insurance and pension fund agreements. It applies the recursive marginal quantization (RMQ) and joint recursive marginal quantization (JRMQ) algorithms outside the framework of traditional ri…

This paper proposes a paradigm shift in the valuation of long term annuities, away from classical no-arbitrage valuation towards valuation under the real world probability measure. Furthermore, we apply this valuation method to two examples of annuity products, one having annual payments linked to a mortality index and…

Framework for transitioning financial models from risk-neutral to real-world measure.

"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices are given by linear forms which do not always correspond to probabilities. We giv…

Simulates risk-neutral markets using neural spline flows.

The price of a stock will rarely follow the assumed model and a curious investor or a Regulatory Authority may wish to obtain a probability model the prices support. A risk neutral probability ${\cal P}^*$ for the stock's price at time $T$ is determined in closed form from the prices before $T$ without assuming a price…

This paper investigates the pricing and hedging of variance swaps under a $3/2$ volatility model. Explicit pricing and hedging formulas of variance swaps are obtained under the benchmark approach, which only requires the existence of the numéraire portfolio. The growth optimal portfolio is the numéraire portfolio and u…

Generative model uses DDPMs for risk-neutral derivative pricing.

A new method is proposed to obtain the risk neutral probability of share prices without stochastic calculus and price modeling, via an embedding of the price return modeling problem in Le Cam's statistical experiments framework. Strategies-probabilities $P_{t_0,n}$ and $P_{T,n}$ are thus determined and used, respective…

Bayesian MS-VAR process improves option pricing models.

We study the pricing of credit derivatives with asymmetric information. The managers have complete information on the value process of the firm and on the default threshold, while the investors on the market have only partial observations, especially about the default threshold. Different information structures are dis…

The paper shows real market exists free lunches with vanishing risks.

We analyse derivative securities whose value is NOT a deterministic function of an underlying which means presence of a basis risk at any time. The key object of our analysis is conditional probability distribution at a given underlying value and moment of time. We consider time evolution of this probability distributi…

This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed process can match exactly the risk-neutral distributions implied by both spot va…

In this article, we consider a Markov process X, starting from x and solving a stochastic differential equation, which is driven by a Brownian motion and an independent pure jump component exhibiting state-dependent jump intensity and infinite jump activity. A second order expansion is derived for the tail probability …

Method determines asset prices in incomplete markets to optimize portfolios.

Generative model prices options and extracts risk-neutral densities.

Deep Hedging learns risk-neutral vol dynamics for option pricing.

Our derivation of the distribution function for future returns is based on the risk neutral approach which gives a functional dependence for the European call (put) option price, C(K), given the strike price, K, and the distribution function of the returns. We derive this distribution function using for C(K) a Black-Sc…

Study asset pricing under model uncertainty with discrete time and states.

Choquet and minimax expectations are equivalent in European option pricing.

In this article we present a continuous time model for natural gas and crude oil future prices. Its main feature is the possibility to link both energies in the long term and in the short term. For each energy, the future returns are represented as the sum of volatility functions driven by motions. Under the risk neutr…

Deriving option prices from operational-time Markov lattices

A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, R_B, of a 2-parameter estimation problem, thus justifying calling C Bayes (B-)price. The result provides new insight in option pricing, among others obt…

In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Follmer-Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation Levy process and the claims pay a predetermined payout at maturity, contingent on…

We construct the term structure of the (forward-looking, US market) equity risk premium from SPX option chains. The method is "model-light". Risk-neutral probability densities are estimated by fitting $N$-component Gaussian mixture models to option quotes, where $N$ is a small integer (here 4 or 5). These densities are…

The paper bounds payoffs and option prices in discrete models.