Related papers: General Duality for Perpetual American Options
Since most of the traded options on individual stocks is of American type it is of interest to generalize the results obtained in semi-static trading to the case when one is allowed to statically trade American options. However, this…
In this paper, we study a version of the perpetual American call/put option where exercise opportunities arrive only periodically. Focusing on the exponential L\'evy models with i.i.d. exponentially-distributed exercise intervals, we show…
There exist several methods how more general options can be priced with call prices. In this article, we extend these results to cover a wider class of options and market models. In particular, we introduce a new pricing formula which can…
We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black-Scholes equation…
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options…
We introduce and study a notion of duality for two classes of optimization problems commonly occurring in probability theory. That is, on an abstract measurable space $(\Omega,\mathcal{F})$, we consider pairs $(E,\mathcal{G})$ where $E$ is…
Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in…
American options in a multi-asset market model with proportional transaction costs are studied in the case when the holder of an option is able to exercise it gradually at a so-called mixed (randomised) stopping time. The introduction of…
The probabilistic equivalent formulation of Dupire's PDE is the Put-Call duality equality. In local volatility models including exponential L\'{e}vy jumps, we give a direct probabilistic proof for this result based on stochastic flows…
In this paper we present a MATLAB version of a non-standard finite difference scheme for the numerical solution of the perpetual American put option models of financial markets. These models can be derived from the celebrated Black-Scholes…
In this work we present a new family of options (mirror options) specially crafted to satisfy the necessities of aggressive speculators. The main ideas behind mirror options are: 1) A product that can be adjusted by the holder to agree with…
This paper presents a derivation of the explicit price for the perpetual American put option time-capped by the first drawdown epoch beyond a predefined level. We consider the market in which an asset price is described by geometric L\'evy…
Put-call parity is a terminal-payoff identity, but its enforcement is capital-using. I study the carry gap, the annualized wedge between option-implied and OIS discount factors, in SPX and RUT index options. Quoted parity is tightly…
In this work, we introduce amortizing perpetual options (AmPOs), a fungible variant of continuous-installment options suitable for exchange-based trading. Traditional installment options lapse when holders cease their payments, destroying…
In this work, we expand the idea of Samuelson[3] and Shepp[2,5,6] for stock optimization using the Bachelier model [4] as our models for the stock price at the money (X[stock price]= K[strike price]) for the American call and put options…
We study perpetual American option pricing problems in an extension of the Black-Merton-Scholes model in which the dividend and volatility rates of the underlying risky asset depend on the running values of its maximum and maximum drawdown.…
We consider the L\'evy model of the perpetual American call and put options with a negative discount rate under Poisson observations. Similar to the continuous observation case as in De Donno et al. [24], the stopping region that…
We establish a super-replication duality in a continuous-time financial model where an investor's trades adversely affect bid- and ask-prices for a risky asset and where market resilience drives the resulting spread back towards zero at an…
We consider the martingale optimal transport duality for c\`adl\`ag processes with given initial and terminal laws. Strong duality and existence of dual optimizers (robust semi-static superhedging strategies) are proved for a class of…
In this paper we present a duality theory for the robust utility maximisation problem in continuous time for utility functions defined on the positive real axis. Our results are inspired by -- and can be seen as the robust analogues of --…