Related papers: Limit Theorems for Partial Hedging Under Transacti…
In a Markovian framework, we consider the problem of finding the minimal initial value of a controlled process allowing to reach a stochastic target with a given level of expected loss. This question arises typically in approximate hedging…
One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This assumption can be fulfilled only in perfectly liquid markets.…
The author presents alternatives to the Black-Scholes european call option pricing model by incorporating different transaction cost structures in the replicating strategy. In particular, an exponentially decreasing structure is proposed…
We extend the application of the Cherny-Shiryaev-Yor invariance principle to a unified Bachelier-Black-Scholes-Merton (BBSM) dynamic pricing model. This extension incorporates the influence of the history of the dynamics (i.e., the path…
Traders and investors involved in an option contract having the underlying stock in range bound are likely to lose their initial investment. Timing in buying an option contract is of capital importance. In a recent article [1] the…
This paper consists of two parts. In the first part we prove the fundamental theorem of asset pricing under short sales prohibitions in continuous-time financial models where asset prices are driven by nonnegative, locally bounded…
We present a parallel algorithm that computes the ask and bid prices of an American option when proportional transaction costs apply to the trading of the underlying asset. The algorithm computes the prices on recombining binomial trees,…
In this paper we introduce a completely continuous and time-variate model of the evolution of market limit orders based on the existence, uniqueness, and regularity of the solutions to a type of stochastic partial differential equations…
We reconsider the problem of option pricing using historical probability distributions. We first discuss how the risk-minimisation scheme proposed recently is an adequate starting point under the realistic assumption that price increments…
We survey some new progress on the pricing models driven by fractional Brownian motion \cb{or} mixed fractional Brownian motion. In particular, we give results on arbitrage opportunities, hedging, and option pricing in these models. We…
This paper studies the problem of option replication in general stochastic volatility markets with transaction costs, using a new specification for the volatility adjustment in Leland's algorithm \cite{Leland}. We prove several limit…
This study investigates enhancing option pricing by extending the Black-Scholes model to include stochastic volatility and interest rate variability within the Partial Differential Equation (PDE). The PDE is solved using the finite…
The usual theory of asset pricing in finance assumes that the financial strategies, i.e. the quantity of risky assets to invest, are real-valued so that they are not integer-valued in general, see the Black and Scholes model for instance.…
On a multi-assets Black-Scholes economy, we introduce a class of barrier options. In this model we apply a generalized reflection principle in a context of the finite reflection group acting on a Euclidean space to give a valuation formula…
This paper studies the equity holders' mean-variance optimal portfolio choice problem for (non-)protected participating life insurance contracts. We derive explicit formulas for the optimal terminal wealth and the optimal strategy in the…
This paper studies arbitrage pricing theory in financial markets with implicit transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded…
Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…
The Black-Scholes model (sometimes known as the Black-Scholes-Merton model) gives a theoretical estimate for the price of European options. The price evolution under this model is described by the Black-Scholes formula, one of the most…
There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise to arbitrage opportunities. We study…
We extend the fundamental theorem of asset pricing to a model where the risky stock is subject to proportional transaction costs in the form of bid-ask spreads and the bank account has different interest rates for borrowing and lending. We…