Related papers: Practical guide to real options in discrete time
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
We construct a binomial tree model fitting all moments to the approximated geometric Brownian motion. Our construction generalizes the classical Cox-Ross-Rubinstein, the Jarrow-Rudd, and the Tian binomial tree models. The new binomial model…
Humans and animals have the ability to reason and make predictions about different courses of action at many time scales. In reinforcement learning, option models (Sutton, Precup \& Singh, 1999; Precup, 2000) provide the framework for this…
This paper gives an arbitrage-free prediction for future prices of an arbitrary co-terminal set of options with a given maturity, based on the observed time series of these option prices. The statistical analysis of such a multi-dimensional…
Within the context of multivariate time series segmentation this paper proposes a method inspired by a posteriori optimal trading. After a normalization step time series are treated channel-wise as surrogate stock prices that can be traded…
We show that, under certain smoothness conditions, a Brownian martingale, when evaluated at a fixed time, can be represented via an exponential formula at a later time. The time-dependent generator of this exponential operator only depends…
We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of…
In this paper we derive tractable formulae for price sensitivities of two-dimensional spread options using Malliavin calculus. In particular, we consider spread options with asset dynamics driven by geometric Brownian motion and stochastic…
It has been recently shown that spot volatilities can be very well modeled by rough stochastic volatility type dynamics. In such models, the log-volatility follows a fractional Brownian motion with Hurst parameter smaller than 1/2. This…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…
We develop closed-form expansions for the implied volatility of VIX options within the class of forward variance models. Our approach builds on weak-approximation techniques for VIX option prices and yields explicit implied volatility…
Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for asset…
In this paper we propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model, based on Taylor expansions and the calculation of mixed exponential-power moments of a Gaussian distribution. Our…
This paper studies an optimal trading problem that incorporates the trader's market view on the terminal asset price distribution and uninformative noise embedded in the asset price dynamics. We model the underlying asset price evolution by…
We introduce a setup of model uncertainty in discrete time. In this setup we derive dual expressions for the super--replication prices of game options with upper semicontinuous payoffs. We show that the super--replication price is equal to…
Financial options are contracts that specify the right to buy or sell an underlying asset at a strike price by an expiration date. Standard exchanges offer options of predetermined strike values and trade options of different strikes…
Executing even moderately large derivatives orders can be expensive and risky; it's hard to balance the uncertainty of working an order over time versus paying a liquidity premium for immediate execution. Here, we introduce the Time Is…
Continuous time systems are often modeled using discrete time dynamics but this requires a small simulation step to maintain accuracy. In turn, this requires a large planning horizon which leads to computationally demanding planning…
A constant weight asset allocation is a popular investment strategy and is optimal under a suitable continuous model. We study the tracking error for the target continuous rebalancing strategy by a feasible discrete-in-time rebalancing…
We investigate the relation between the fair price for European-style vanilla options and the distribution of short-term returns on the underlying asset ignoring transaction and other costs. We compute the risk-neutral probability density…