A Price Hedging Model in Dynamic Market

Abstract

Problem statement: Pricing is a problem when a firm has to set a price for the first time. This happens when the firm develops or acquires a new product, introduces its regular product into a new distribution or geographical area, or enters bids on the new contract work. Many companies try to set the price to maximize current profits. They estimate the demand and costs associated with alternative prices and choose the price that maximizes current profit, cash flow, or rate of return on investment. There are, however, some problems associated with the current profit maximizing approach as it assumes that the firm knows its demand and cost functions; in reality, demand is difficult to estimate and is unpredictable. Approach: Due to demand’s unpredictability, we assume that it follows a lognormal random walk. Based on this, we develop a mathematical pricing processes model by stochastic calculus, which is similar to the financial process mathematical model. From Ito’s lemma, a product’s profit correlates with demand, is also unpredictable and follows a random walk. Such random behavior is the marketing risk. Results: By choosing a price strategy to eliminate randomness, called price hedging, we obtain risk-free profit determined by the Black-Scholes equation. This riskless profit, which is predictable, is the same we would get by putting the equivalent amount of cash in a risk-free interest-bearing account. Conclusion: From price hedging and the Black-Scholes equation, we determine the basic product price, which changes with time and demand.