Class 1 - State Prices Flashcards
What do digital options provide?
PV of a portfolio with: Sure unit in one state, and zero in any other
What is the state price
Value of digital options
Value of an asset (depending on a digital option)
Sum of payoffs in each state x Value of digital option in each state
V =
Xu x Iu + Xd x Id
A portfolio of two digital options that pays 1 in u and 1 in d
1 / 1+rf
rf =
1 / Iu + Id
Iu and Id reflect:
Probability and Dicount Rate
Iu =
Value of digital option “up”
PV of a risk-free CF =
Soma de todos os Pt x Xt, onde:
- Pt = Discounted monetary unit = 1/1+rf
- Xt = FV risk-free CF
PV of a risky CF =
Soma de todos os P(beta)t x Xt, incorporating market risk in discount
ps (Probability) =
Is x (1+r)
Note: Is = value of digital option
V (with ps) =
1/1+r x Sum of ps x Xs
Value of asset = weighted average of discounted cfs, where probability represents weight
V (reality) =
Discounted expected payoff of the asset
What is a derivative?
An asset with a payoff that is a function of the value of an underlying
Put Call parity formula
Put + S = Call + Discounted Strike
