dc66e42ec4
Categories now match folder names (15 canonical values). Types normalized to 25 canonical values per VAULT_MAP.md spec. Context-aware mapping: W-2s→tax-form, lease files→lease, vet records→vet, etc.
962 B
962 B
type, category, person, date, source
| type | category | person | date | source |
|---|---|---|---|---|
| medical-form | academic | 2017-04-29 | options_pricing_notes.jpg |
Q1 - Options Pricing (Binomial Model)
(a)
Stock price tree:
- S₀ = 100
- Up: 130
- Down: 80
Payoff tree (put option, strike = $20 implied):
- Up: 0
- Down: $20
System of equations (replicating portfolio):
\begin{cases}
130\alpha + 1.1\beta = 0 \\
80\alpha + 1.1\beta = 20
\end{cases}
Solutions:
\alpha = -0.4
\beta = 47.27
Put price:
P = -100 \times 0.4 + 47.27 = \boxed{\$7.27}
(b)
Payoff tree (call option):
- Up: 30
- Down: 0
System of equations (replicating portfolio):
\begin{cases}
120\alpha + 1.1\beta = 30 \\
80\alpha + 1.1\beta = 0
\end{cases}
Solutions:
\alpha = 0.6
\beta = -43.64
Call price:
C = 60 - 43.64 = \boxed{\$16.36} > 15 \text{ Under priced.}
Buy call and sell/short synthetic put.
Or, put-call parity:
C = S_0 + P - \frac{X}{(1+r)^t} = \$16.36 > 15