Binomial Model
Formula
|
Remarks
|
VOC = P x Cu +
(1 – P) x Cd
R
|
Where,
R = 1 + Rf
Cu = Call Upside
Gain
Cd = Call Downside Gain
Pu = Put Upside
Gain
Pd = Put Downside Gain
d = ds (expected downside price divided by spot
price)
s
u = us (expected upside price divided by spot
price)
s
|
VOC = P x Pu +
(1 – P) x Pd
R
|
|
P = R – d
U – d
|
|
Value of American
Option = Max of Discounted Value or Intrinsic Value
|
Put Call Parity
Theory (PCPT)
Spot Price + Value
of Put = Value of Call + Present Value of Exercise/Strike Price
PCPT is the
relationship between European Call and Put Option on the same stock, the
maturity period and EP is same.
The PCPT equation
is made to prevent arbitrage profit. If LHS ≠ RHS, then there would arise
arbitrage profit.
LHS Þ SP + VOP (Protective Put – S+, P+)
RHS Þ VOC + PV of EP (Fiduciary Call – C+, ZCB+)
Risk Neutral
Valuation
The Price of an
option is independent of the risk preference of Investor Called risk-neutral
valuation.
Black Scholes
Model
Formula
|
Remarks
|
European Call
Option = SP x N (d1) – PV of EP x N (d2)
|
Where,
Ln = Natural Log
SP = Spot Price
EP = Exercise
Price
R= Rate of
Interest
T = time
|
d1 =
ln (SP) + (r + .5 σ2) x t
EP………………..
σ√t
|
|
d2 = d1
- σ√t
|
|
Assumption of
Block Scholes Model
European options
are considered.
No Transaction
Costs.
Short Term
interest rates are known and constant.
Stocks don’t pay
dividend.
Stock Price
Movement is similar to random walk.
Stock returns are
normally distributed over a period of time.
Variance of
return is constant over the life of an option.
|
|
When Probability
distribution or probable market price is given for market price of share on
expiration then value of option will be calculated as follows: -
Value of Option =
(AMP –EP) x Probability + (AMP – EP) x Probability + ……………….. (.i.e. we should
check individually)
Future/(1 + Rf)
= Spot Price + PV of Storage – PV of Convince Yield
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