FBE559.slides.07

11 11 bond 06 04 1 1 1 11 11 11 call with

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ere du ( or dd ) is the price of the digital up (or down) option. Simple examples Stock: 0.6 0.4 (75) + (25) = 50. 1.1 1.1 Bond: 0.6 0.4 1 (1) + (1) = . 1.1 1.1 1.1 Call with strike of $50: 0.6 0.4 15 (25) + (0) = = 13.64. 1.1 1.1 1.1 Put with strike of $36: 0.4 0.6 (0) + (11) = 4. 1.1 1.1 Risk Neutral Probabilities Since du + dd = 1/(1 + r ) = 1/1.1, we can write: PV(CF ) dd du CFu + CFd du + dd du + dd = (du + dd ) = qu CFu + qd CFd 1+r where qu = du = 0.6, du + dd qd = dd = 0.4. du + dd We call qu and qd risk-adjusted probabilities because they are positive sum to one. Risk Neutral Pricing Thus, the price of a security equals the expected payoff using the risk-adjusted probabilities, discounted at the risk-free rate: PV(CF ) = EQ [CF ] qu CFu + qd CFd = . 1+r 1+r This is called the risk-neutral pricing formula. Risk-adjusted probabilities are (normalized for time-value of money) prices of digital options. They are different from the true probabilities. The market in general is not risk-neutral. Risk Neutral Pricing Note that in general we are making two errors here: 1 people discou...
View Full Document

Ask a homework question - tutors are online