1a The current price of a stock is 43 and the continuously c

1a) The current price of a stock is $43, and the continuously compounded risk-free rate is 7.5%. The stock pays a continuous dividend yield of 1%. A European call option with a exercise price of $35 and 9 months until expiration has a current value of $11.08. What is the value of a European put option written on the stock with the same exercise price and expiration date as the call? Answers: a. $5.17 b. $3.08 c. $1.49 d. $2.50 e. $–11.08

1b)

Suppose a stock’s price is $25, and the continuously compounded interest rate is 4.5%. The stock does not pay dividends. To ensure that arbitrage is not possible, what should be the difference (C – P) between the price of a 6-month $30-strike European call and the price of a 6-month $30-strike European put?

$–4.89

$–3.73

$–4.33

$–5.00

$–5.56

1c)

Suppose the exchange rate is $1.23/€, the euro-denominated continuously compounded interest rate is 8%, the U.S. dollar-denominated continuously compounded interest rate is 2%, and the price of a 6-month $1.30-strike European call on the euro is $0.0839. What is the value of a 6-month $1.30-strike European put on the euro?

$0.2184

$0.1892

$0.1539

$0.1152

$0.1740

Please explain the steps and forumulas. Thank you.

Solution

Greetings,

1. As per put call parity (PCP), the following relation must hold good for european options on the same underlying having same exercise and same maturity -

Price of Put + Price of Underlying = Price of call + PV of exercise value

PV of EV

risk free rate = 7.5% continous p.a

risk free rate = 7.5*9/12 = 5.625% for 9 months

PV of EV = 35/e^0.05625 = 33.0844

Price of stock has to be taken ex dividend. Since the dividend yield is given, so we need to discout share price by 1% for 9m ie 0.75%

Ex dividend share price = 43/e^0.0075 = 42.68

Re arranging above formula,

Value of put = 11.08 + 33.08 - 42.68 = 1.48 or rounded off to 1.49

2.Same formula of put call parity to be used.

C-P = Price of underlying - PV of EV

PV of EV = 30/e^0.0225* = 29.3312

C-P = 25 - 29.3312 = -4.3312

* 0.045* 6/12 = 0.0225

3. same formulas to be used.

In case of foreign currency options, the rate of base currency is equivalent to dividend yield ie Euro rate is used to make spit price ex dividend.

Ex dividend spot price = 1.23/e^0.04* = 1.1818

The rate on price currency is used as rf and used to find out PV of EV.

PV of EV = 1.30/e^0.01* = 1.2870

Value of put = 0.0839 + 1.2870 - 1.1818 = 0.1891 rounded off to 0.1892

Note - Every where exponential function is to be used as rate is continuously compounded.

* 0.08* 6/12 = 0.04

0.02* 6/12 = 0.01