Question

Imagine that you are unable to short-sell a particular stock. Using put-call parity, replicate a short position in the stock, assuming that the stock pays no dividends,

there is a put and a call option, both of which have the same exercise price, K, and the same time to expiration, T. You are able to borrow and lend the

continuously compounded risk free rate, r.

Answer #1

Put - Call parity can be termed as :

Where C = Position in a call option,

KerT = Position in the bond with face value equal to the strike price of the option K, invested at r(continuous compounded risk free rate) for time period T (option expiration T).

P = Position in the put option

and, S = Position in the stock.

Given to us that we need to derive the parity in such a way that we are able to short the stock. The equation for the same is:

S- refers to taking a short position in the stock. This can be done by simply taking a LONG POSITION in the PUT OPTION (P+), a SHORT POSITION IN CALL OPTION and BORROWING MONEY equal to the strike price K for time period T at risk free rate r.

Assume that put options on a particular stock are very thinly
traded and have very high transaction costs with a large bid-ask
spread.
You desire to sell a 3-month out option on this particular stock
(sell to open) but want to avoid the high transactions cost. you
understand put-call parity. Assume that we are referring to
European style options
A) using the principles of put call parity, how could you create
a "short synthetic put" by transacting the stock, the...

A synthetic long call option can be created
from put-call parity relation as follows:
Buy the call option, sell the stock, and sell a bond that pays
the option’s exercise price at maturity
Buy the call, sell the stock, and buy a bond that pays the
exercise price at maturity
Sell the call, buy the stock, and sell a bond that pays the
exercise price at maturity
Buy the stock, buy the put, and sell a bond that pays the...

2) Discuss how a long call position in a particular stock
would
differ from a short put position in the same stock with the
same
strike price and the same expiration date.
2a) Explain why a call option on a specific stock with a
specific
strike price and expiration date might be worth much more
than
another call option on a different stock having the same
stock
price, the same option strike price, and the same expiration
date.

Assume that the stock price is $56, call option price is $9, the
put option price is $5, risk-free rate is 5%, the maturity of both
options is 1 year , and the strike price of both options is 58. An
investor can __the put option, ___the call option, ___the stock,
and ______ to explore the arbitrage opportunity.
sell, buy, short-sell, lend
buy, sell, buy, lend
sell, buy, short-sell, borrow
buy, sell, buy, borrow

Based on the put-call parity relationship you want to make an
arbitrage profit by selling a call, buying a put, and taking a
leveraged equity position.
Stock proce = $100
Call price (6-month maturity with strike price of $110) =
$5
Put price (6-month maturity with strike price of $110) =
$8
Risk free interest rate (continuously compounded) = 10%
If the stock price at maturity is $120, how much do you earn
from all these positions?

Use the following option prices for options on a stock index
that pays no dividends to answer questions. The options have three
months to expiration, and the index value is currently 1,000.
STRIKE (K)
CALL PRICE
PUT PRICE
975
77.716
43.015
1000
64.595
X
1025
53.115
67.916
a. Using put-call parity, what is the
implied continuously compounded interest rate?
Using put-call parity, what is the correct price for the put
option with a strike of
1,000? (i.e., what is X?)

For a European call option and a European put option on the same
stock, with the same strike price and time to maturity, which of
the following is true?
A) Before expiration, only in-the-money options can have
positive time premium.
B) If you have a portfolio of protected put, you can replicate
that portfolio by long a call and hold certain amount of risk-free
bond.
C) Since both the call and the put are risky assets, the
risk-free interest rate...

For a European call option and a European put option on the same
stock, with the same strike price and time to maturity, which of
the following is true?
A) When the call option is in-the-money and the put option is
out-of-the-money, the stock price must be lower than the strike
price.
B) The buyer of the call option receives the same premium as the
writer of the put option.
C) Since both the call and the put are risky...

It has been observed that the put-call parity relation is often
violated in practice – that is, Put price > Synthetic put price
= Call price + Present value of strike price –Underlying stock
price + Present value of dividends. In other words, if one buys the
synthetic put by buying call, buying a risk-less bond that pays the
strike price at the maturity, and short-selling the underlying
stock and sells the put with the same strike price as the...

a) It has been observed that the put-call parity relation is
often violated in practice – that is, Put price > Synthetic put
price = Call price + Present value of strike price – Underlying
stock price + Present value of dividends. In other words, if one
buys the synthetic put by buying call, buying a risk-less bond that
pays the strike price at the maturity, and short-selling the
underlying stock and sells the put with the same strike price...

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