Valuation option Using binomal

Question 1

Valuing a Call Option example:

Answer 1

S0 = 50

Upmove = 60
Downmove = 42

Short Call option at 55

Up move = 60-55 = 5
Downmove = 0 (received the premium)

Stock call ratio for portfolio that has the same down and up value:

ValueUp = hStockUp - CallUp = hSdn-Cdn

h = Hedge Ratio

Ex. h of .278 means you need .278 stock for each call short

Question 2

What is the premium of your call?

Answer 2

Pv of expected Payoffs

Question 3

Risk neutral Probability of a Up Move formula

And down move

Answer 3

Pup = 1+Rf - Down
——————-
Up - Down

PDown = 1- Pup

Question 4

How we can evaluate a call option regardless of the underlying asset expiration price?

Answer 4

Same value at option expiration
Whether if is an
Up move or
Down move

Pv = discounted Pv of certain payment, which can be used to value the option

Question 5

Combining options and U/L assets in specific ratio will produce:

Answer 5

Risk free future payments

Question 6

Hedge Rate

Answer 6

h = (Up value - X)
———————-
Up value - Down Value

Question 7

Portfolio value formula and reading

Answer 7

h SUp - CallUp = hSdown - Call Down

Reading:

What is the value of my portfolio regardless my Stock goes a determined amount up and determined amount down

Question 8

Risk neutral Price Step by Step

Answer 8

1- bynomial tree

So x up factor —> One year time

So x down factor —> One year time

2- Evaluate the Payoff (Call or put)

Stock goes Up payoff
Call = St - X
Put = 0, X - St

Stock goes down
Call = 0, St-X
Put = X - St

Applie the Risk Neutral Pricing Formula

          (1+ Rf ) - P down RnP=  ——————————
               P Up - P Down

C0=(RnP) x (Payoff Up) + (1-RnP)(PayoffDn)
—————————————————
(1+Rf)

Rnp = Risk Neutral Price

Question 9

What is the effect of Probability in Binomial Valuing of a Option

Answer 9

NONE!

What matters is the possible value (volatility)
Not the fucking probability