Math Problem Statement

make a problem like Consider a non-dividend-paying stock whose current price is $120 per share. The stock has the volatility equal to.2. Let the continuously-compounded risk-free interest rate be.05. You model the evolution of this stock over the next quarter with a forward binomial tree. What is the price of a $122-strike three-month put on the above stock consistent with this model?. Do not simply copy-paste the narrative, just changing out the numbers. Make the problem your own by creating your own story. Try to make the new problem as close as possible in difficulty to the problem from the exam. 

Solution

Here’s a new problem inspired by your request:


Problem:

Consider a non-dividend-paying stock of a technology company, whose current price is $85 per share. The stock has an annualized volatility of 0.25. The continuously-compounded risk-free interest rate is 0.03. You are tasked with modeling the evolution of this stock over the next two months using a forward binomial tree.

What is the price of a $87-strike two-month put option on the stock consistent with this model?


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Math Problem Analysis

Mathematical Concepts

Financial Mathematics
Options Pricing
Binomial Tree Models
Volatility
Risk-Free Interest Rates

Formulas

Binomial Option Pricing Formula
Risk-Neutral Valuation
Put Option Payoff Formula: max(K - S, 0)

Theorems

Risk-Neutral Valuation Theorem
No-Arbitrage Principle

Suitable Grade Level

Undergraduate/Graduate Level (Finance or Mathematics)