Draw the payout functions for the two option

Assignment Help Financial Econometrics

Reference no: EM131243648

The Black-Scholes formula by change of numeraire Let St be the price at time t of a stock that pays no dividends.

(a) Draw the payout functions for the two options

(i) KI{ST ≥ K}

(ii) STI{ST ≥ K}

where I{} is the indicator function. Which linear combination of (i) and (ii) gives the payout of a call option?

(b) Suppose the risk-neutral distributions of S_T conditional on S_t with respect to the money market and stock numeraires are given by the answers to Question 5(c) and (e), respectively. Price options (i) and (ii) in terms of the normal cumulative distribution function Φ (·) using the money market numeraire for (i) and the stock numeraire for (ii). Hence derive immediately the Black-Scholes equation for the price of a call option.

Question 5(c)

(c) Suppose the risk-neutral distribution of S_T conditional on S_t, with respect to the money market numeraire, is lognormal (log S_t + ν(T - t), σ²(T - t)), that is, log S_T | S_t ∼ N(log S_t + ν(T - t), σ²(T - t)). Use a martingale condition for S_T/M_T to find ν in terms of σ and r, the constant, continuously compounded interest rate.

Reference no: EM131243648

Questions Cloud

What is the income elasticity of demand for cigarettes : What is the elasticity of demand for cigarettes with respect to price? Is it statistically significant? If so, is it statistically different from one?

Next caper somewhere on pennsylvania avenue : Holy digits Batman! The Riddler is planning his next caper somewhere on Pennsylvania Avenue. In his usual sporting fashion, he has left the address in the form of a puzzle. The address on Pennsylvania is a four-digit number where:

Should the interest rate variable be retained in the model : See if the Cobb-Douglas production function fits the data given in the table and interpret the results. What general conclusion do you draw?

Interest on a loan is paid on a declining balance : Interest on a loan is paid on a declining balance, and hence a loan with an interest rate of, say, 14 percent can cost significantly less than 14 percent of the balance. Write a program that takes a loan amount and interest rate as input and then ..

Draw the payout functions for the two option : The Black-Scholes formula by change of numeraire Let St be the price at time t of a stock that pays no dividends. - Draw the payout functions for the two options.

Why is a correlation the most appropriate statistic : What is the correlation between student anxiety scores and number of study hours? Select alpha and interpret your findings. Make sure to note whether it is significant or not and what the effect size is.

Discuss the properties of these models : Where Yt = sales at time t and t = time, measured in years. The first model postulates that sales is a linear function of time, whereas the second model states that it is a quadratic function of time.

Calculate the price at time t of the digital caplet : Calculate the price at time t of the digital caplet that pays α at time (T + α) if LT > K, and zero otherwise, under the two different models (I) and (II).

Can you explain in your own words what kant might have meant : Kant famously--and controversially--argued that some knowledge is "synthetic a priori." Can you explain in your own words what Kant might have meant by this, and can you give an example of the sort of knowledge that Kant believed possessed this st..

User Account

All Pages