Related papers: Pricing Derivatives on Multiscale Diffusions: an E…
We consider the problem of choosing prices of a set of products so as to maximize profit, taking into account self-elasticity and cross-elasticity, subject to constraints on the prices. We show that this problem can be formulated as…
As markets have digitized, the number of tradable products has skyrocketed. Algorithmically constructed portfolios of these assets now dominate public and private markets, resulting in a combinatorial explosion of tradable assets. In this…
We construct a sequence of functions that uniformly converge (on compact sets) to the price of Asian option, which is written on a stock whose dynamics follows a jump diffusion, exponentially fast. Each of the element in this sequence…
We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that…
This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and…
We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in…
Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility…
In this article, we combine replication pricing with expectation pricing for derivative trades that are partially collateralized by cash. The derivatives are replicated by underlying assets and cash, using repurchasing agreement (repo) and…
The multidimensional Uncertain Volatility Model leads to robust option pricing problems under joint volatility and correlation uncertainty. Their numerical resolution quickly becomes challenging because the associated stochastic control…
We consider call option prices in diffusion models close to expiry, in an asymptotic regime ("moderately out of the money") that interpolates between the well-studied cases of at-the-money options and out-of-the-money fixed-strike options.…
We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for…
We consider the pricing and hedging of exotic options in a model-independent set-up using \emph{shortfall risk and quantiles}. We assume that the marginal distributions at certain times are given. This is tantamount to calibrating the model…
We design three continuous--time models in finite horizon of a commodity price, whose dynamics can be affected by the actions of a representative risk--neutral producer and a representative risk--neutral trader. Depending on the model, the…
We present a numerical method for the frequent pricing of financial derivatives that depends on a large number of variables. The method is based on the construction of a polynomial basis to interpolate the value function of the problem by…
A variance swap is a derivative with a path-dependent payoff which allows investors to take positions on the future variability of an asset. In the idealised setting of a continuously monitored variance swap written on an asset with…
We propose a new forward-backward stochastic differential equation solver for high-dimensional derivatives pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo…
Neural networks with sufficiently smooth activation functions can approximate values and derivatives of any smooth function, and they are differentiable themselves. We improve the approximation capability of neural networks by utilizing the…
Given a multi-dimensional It\^{o} process whose drift and diffusion terms are adapted processes, we construct a weak solution to a stochastic differential equation that matches the distribution of the It\^{o} process at each fixed time.…
We present a high-level framework that explains why, in practice, different pricing models calibrated to the same vanilla surface tend to produce similar valuations for exotic derivatives. Our approach acts as an overlay on the Monte Carlo…
The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in…