Financial Mathematics 1 - Homework 10

Instructor: Dr. Le Nhat Tan

1 Group Members

  1. Nguyen Minh Quan - MAMAIU19036
  2. Tran Viet Hang - MAMAIU18079
  3. Le Nguyen Dang Khoa - MAMAIU19008

For further discussion, please contact us via email: quannguyenuw@gmail.com.

2 Options - Slides

2.1 Slides 14

Let the current stock price be $35 and the European put option is in-the-money by $3.50. Find the corresponding strike price.

Solution:

2.2 Slides 16

Consider a long call option with strike price K = $100. The current stock price is \(S_t\) = $105 and the call premium is $10.

  1. What is the intrinsic value of the call option at time t?

  2. Find the payoff and profit if the spot price at the option expiration date T is ST = $120.

  3. Draw the payoff and profit diagrams.

Solution:

2.3 Slides 18

Consider a long put option with strike price K = $100. The current stock price is \(S_t\) = $80 and the put premium is $5.

  1. What is the intrinsic value of the put option at time t?

  2. Find the payoff and profit if the spot price at the option expiration date T is \(S_T\) = $75.

  3. Draw the payoff and profit diagrams.

Solution:

2.4 Sldies 20

2.4.1 1

Consider a short position in a call option (a short call option) with strike price K = $100. The current stock price is \(S_t\) = $105 and the call premium is $10.

  1. What is the intrinsic value of the short call option at time t?

  2. Find the formula of the payoff and profit of the option at expiry. Compute the payoff and profit if the spot price at the option expiration date T is \(S_T\) = $120.

  3. Draw the payoff and profit diagrams.

Solution:

2.4.2 2

Consider a short put option with strike price K = $100. The current stock price is \(S_t\) = $80 and the call premium is $5.

  1. What is the intrinsic value of the short put option at time t?

  2. Find the formula of the payoff and profit of the option at expiry. Compute the payoff and profit if the spot price at the option expiration date T is \(S_T\) = $75.

  3. Draw the payoff and profit diagrams.

Solution: