{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

50. Lower and upper bounds for call and put options and put call parity.

# 50. Lower and upper bounds for call and put options and put call parity.

This preview shows pages 1–5. Sign up to view the full content.

University of California, Los Angeles Department of Statistics Statistics C183/C283 Instructor: Nicolas Christou Lower and upper bounds for the price of a European calls and puts A. Lower bound for the price of a European call: Time t = 0 Payoﬀ at time t = 1 S 1 > E S 1 E Portfolio A : Buy 1 call - C S 1 - E 0 Cash (lend) - E 1+ r + E + E Total S 1 E Portfolio B : Buy 1 share - S 0 S 1 S 1 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
B. Lower bound for the price of a European put: Time t = 0 Payoﬀ at time t = 1 S 1 E S 1 < E Portfolio A : Buy 1 put - P 0 E - S 1 Buy 1 share - S 0 S 1 S 1 Total S 1 E Portfolio B : Cash (lend) - E 1+ r + E + E 2
C. Upper bound for the price of a European call: No matter what happens, C S 0 If not, there will be an opportunity for a riskless proﬁt by buying the stock and selling the call option. How? Suppose C > S 0 . Time t = 0 Payoﬀ at time t = 1 S 1 > E S 1 E Sell 1 call C E - S 1 0 Buy 1 stock - S 0 S 1 S 1 Total C - S 0 E S 1 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
D. Upper bound for the price of a European put: No matter what happens, P E 1+ r . If not, there will be an opportunity for a riskless proﬁt by selling the put and investing
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the proceeds at the risk free interest rate. How? Suppose P > E 1+ r . Time t = 0 Payoﬀ at time t = 1 S 1 ≥ E S 1 < E Sell 1 put P > E 1+ r S 1-E 4 Put-Call Parity This is an important relationship between the price of a put and the price of the call. A put and the underlying stock can be combined in such a way that they have the same payoﬀ as a call at expiration. Consider the following two portfolios: Portfolio A : Buy the call and lend an amount of cash equal to E 1+ r . Portfolio B : Buy the stock, buy the put. This is shown on the table below: Time t = 0 Payoﬀ at time t = 1 S 1 > E S 1 ≤ E Portfolio A : Buy 1 call-C S 1-E Lend cash-E 1+ r E E Total-C-E 1+ r S 1 E S 1 ≥ E S 1 < E Portfolio B : Buy 1 put-P E-S 1 Buy 1 stock-S S 1 S 1 Total-P-S S 1 E 5...
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

50. Lower and upper bounds for call and put options and put call parity.

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online