We explicitly compute closed formulas for the minimal variance hedging strategy in discrete time of a European option and for the variance of the corresponding hedging error under the hypothesis that the underlying asset is a martingale following a Geometric Brownian motion. The formulas are easy to implement, hence the optimal hedge ratio can be employed as a valid substitute of the standard B...

We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical varianc...

In practice, all option strategies are decided in advance, given the investor’s belief of the stock price. In this paper, instead of deciding in advance the most appropriate hedging option strategy, an LP problem is formulated, by considering all significant Greek parameters of the Black-Scholes formula, such as delta, gamma, theta, rho and kappa. The optimal strategy to select will be simply d...

Under the assumptions of the market of Black and Scholes, options are redundant since, through the classic Black-Scholes delta hedging argument, they can be replaced by an equivalent combination the risky asset underlying the option and a risk free asset. We show that options are not redundant when small proportional transaction costs of size ε are added to the model, which provides mathematica...

This article shows that the one-state-variable interest-rate models of.There are an enormous number of derivative securities being traded in financial markets. And just define those securities that we shall be pricing. Definition.We present a model for pricing and hedging derivative securities and option portfolios in an. In this equation, the pricing volatility is selected dynamically from.Bec...

The correction in value of an OTC derivative contract due to counterparty risk under funding constraints, is represented as the value of a dividend-paying option on the value of the contract clean of counterparty risk and excess funding costs. This representation allows one to analyze the structure of this correction, the so-called Credit Valuation Adjustment (CVA for short), in terms of replac...

Options with discontinuous payoffs are generally traded above their theoretical Black–Scholes prices because of the hedging difficulties created by their large delta and gamma values. A theoretical method for pricing these options is to constrain the hedging portfolio and incorporate this constraint into the pricing by computing the smallest initial capital which permits superreplication of the...

• We develop a gated neural network based option valuation model. It satisfies no-arbitrage constraints and boundary conditions for European options. A separate is constructed to predict option-implied volatilities. Empirically, the model beats popular alternatives in predicting prices hedging. In this paper, we start from pricing novel hybrid (hGNN) adopt multiplicative structure of hidden lay...

Options or “privileges” as they were known in early 19th Century America actually appeared on the financial scene around the same times as stocks. Initially, there were numerous problems with the trading of options. The terms of the contract were different from contract to contract, contracts had to be exercised in person, and there really was no secondary market to trade. Options were eventual...

We consider option hedging and pricing for a large agent. The large agent affects the market’s demand-supply equilibrium and, therefore, the market prices of financial instruments. By assuming a specific large agent’s effect function for the underlying asset we derive the corresponding effect function for call options on that asset. As we show, the price of a call option in our model is the sol...