corp_Ch22_09

corp_Ch22_09 - CLASS NOTES WEEK IX BM Ch.22 Valuing options...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
IRPGEN424 Corporate Finance Alex Kane 1 CLASS NOTES WEEK IX BM Ch.22 Valuing options
Background image of page 1

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

View Full DocumentRight Arrow Icon
IRPGEN424 Corporate Finance Alex Kane 2 Financial engineering The technique of creating and valuing derivative assets, including exotic derivatives (e.g., Asian, barrier, lookback, caput, quantos, digital). Financial engineering specialists must be highly skilled in math and statistics There is a number of graduate programs in financial engineering (e.g. MFE at Berkeley)
Background image of page 2
IRPGEN424 Corporate Finance Alex Kane 3 Risk free portfolios and arbitrage A standard method in financial engineering is to identify a package of securities that make up a risk-free Pf A risk-free Pf is easy to value because the discount rate is observable. Risk-free portfolios most assuredly will be arbitrage-priced First concept: Option Delta Stock (S) and Call (C): If CF to long C across states of the world changes in fixed proportions to CF to long S, say 2 to 3, we can construct a risk-free Pf Write (sell) 3 calls and buy 2 shares This ratio (2/3) is called the hedge ratio or option delta
Background image of page 3

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

View Full DocumentRight Arrow Icon
IRPGEN424 Corporate Finance Alex Kane 4 CF from call and stock, and implied delta initial stock price S=50 initial call price = C stock price at the “up” stage u*S = 100 stock price at the “down” stage d*S = 25 CF from option C u = 50 CF from option C d = 0 notation: u =1+r u , d= 1+r d , f = 1+r f In this example, u=2, d=0.5 ( stock can double or halve) call delta=hedge ratio= C/ S ( C u –C d )/ (u*S–d*S) = 50/75 = 2/3 need 2 shares for 3 calls to set up arbitrage portfolio strike price X = 50
Background image of page 4
IRPGEN424 Corporate Finance Alex Kane 5 Using call delta to Price by arbitrage The objective is to find C Investment strategy: write 1 call, buy shares (scale up if needed to round units) Payoff on maturity Portfolio Cost d*S = 25 u*S = 100 write 3 calls –3C –3Cd = 0 –3Cu = –150 buy 2 shares 2S=100 2u*S = 50 2u*S = 200 100–3C 50 50 We have engineered a risk-free pf, can discount by f=1+r f = 1.1 100–3C = 50/1.1 => C = (100 – 50/1.1)/3 = 18.18 This arbitrage-based solution does not depend on risk aversion or any equilibrium risk-return relationship
Background image of page 5

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

View Full DocumentRight Arrow Icon
IRPGEN424 Corporate Finance Alex Kane 6 Variables we didn’t use to value the call Note that the probabilities of up/down states are not necessary for the solution. Neither is the required return on the stock The probabilities and required rate of return are implied by the price of the stock, given the two possible outcomes. Put differently, probabilities and the required return are implicit in the stock price We can value the call from a no-arbitrage requirement (similar story: TV game)
Background image of page 6
Corporate Finance Alex Kane 7 Variables in valuation of derivatives False intuition : a critical variable in the value of a derivative is the expected return on the underlying However: the expected return on the underlying is NOT on the list of relevant variables Variables that do affect derivative prices:
Background image of page 7

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

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/06/2010 for the course IRPS IRGN 410 taught by Professor Kane during the Fall '09 term at UCSD.

Page1 / 25

corp_Ch22_09 - CLASS NOTES WEEK IX BM Ch.22 Valuing options...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online