Related papers: Mirror Options
In an incomplete market, including liquidly-traded European options in an investment portfolio could potentially improve the expected terminal utility for a risk-averse investor. However, unlike the Sharpe ratio, which provides a concise…
In some options markets (e.g. commodities), options are listed with only a single maturity for each underlying. In others, (e.g. equities, currencies), options are listed with multiple maturities. In this paper, we provide an algorithm for…
An open market is a subset of an entire equity market composed of a certain fixed number of top capitalization stocks. Though the number of stocks in the open market is fixed, the constituents of the market change over time as each…
We investigate upper and lower hedging prices of multivariate contingent claims from the viewpoint of game-theoretic probability and submodularity. By considering a game between "Market" and "Investor" in discrete time, the pricing problem…
The aim of this work is an analytic investigation of differential equations producing mirror maps as well as giving new examples of mirror maps; one of these examples is related to (rational approximations to) $\zeta(4)$. We also indicate…
We correct a mistake in the published version of our paper. Our new conclusion is that the "implied leverage effect" for single stocks is underestimated by option markets for short maturities and overestimated for long maturities, while it…
Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the…
Market making of options with different maturities and strikes is a challenging problem due to its highly dimensional nature. In this paper, we propose a novel approach that combines a stochastic policy and reinforcement learning-inspired…
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…
We present two concepts of deformable mirror to compensate for first order optical aberrations. Deformation systems are designed using both elasticity theory and Finite Element Analysis in order to minimize the number of actuators. Starting…
By using a variational principle we find a necessary and sufficient condition for an operator to majorise the parallel sum of two positive definite operators. This result is then used as a vehicle to create new operator inequalities…
In this work, we aim to gain a better understanding of the volatility smile observed in options markets through microsimulation (MS). We adopt two types of active traders in our MS model: speculators and arbitrageurs, and call and put…
This paper mainly discusses the American option's hedging strategies via binomialmodel and the basic idea of pricing and hedging American option. Although the essential scheme of hedging is almost the same as European option, small…
In informationally efficient financial markets, option prices and this implied volatility should immediately be adjusted to new information that arrives along with a jump in underlying's return, whereas gradual changes in implied volatility…
We present a \emph{mirror-free} mirror prox (MFMP) algorithm, which extends the classic approach of Nemirovski (2004) to allow for proximal-like updates without the explicit need for a mirror map. We further analyze the convergence of our…
Real life hedging in the Black-Scholes model must be imperfect and if the stock's drift is higher than the risk free rate, leads to a profit on average. Hence the option price is examined as a fair game agreement between the parties, based…
Counterfactual explanations are emerging as an attractive option for providing recourse to individuals adversely impacted by algorithmic decisions. As they are deployed in critical applications (e.g. law enforcement, financial lending), it…
This paper investigates the equilibrium portfolio selection for smooth ambiguity preferences in a continuous-time market. The investor is uncertain about the risky asset's drift term and updates the subjective belief according to the…
We consider a new family of derivatives whose payoffs become strictly positive when the price of their underlying asset falls relative to its historical maximum. We derive the solution to the discretionary stopping problems arising in the…
We generalize our theorems in "Mirror Principle I" to a class of balloon manifolds. Many of the results are proved for convex projective manifolds. In a subsequent paper, Mirror Principle III, we will extend the results to projective…