Question

Can you please explain no pricing arbitrage theory for option pricing in detail? Take an example and do it excel. Please keep it neat and simple. Show all formulas in excel.  

Answer 1

There are different options pricing therories in which no arbitrage bound provides no speculation opportunities and hence is the least riskiest at the same time.The options (Put/Call) prices are obtained by replicating their underlying assets and other risk free instruements available in the market.

The same can be explained by taking an example of a call option. The same will be exercised at strike price (X). Hence,

Intrinsic value = Max [S-X,0].

In other it is a way of setting a lowe bound for call such that C > Max [S-X,0]. This is the necessary condition for this method to work.

This equation satisfies for the current period ( t=0), but if we take t into consideration, it can be further illustrated as

C > Max[S-PV(X), 0] more or equal to Max[S-X, 0]

PV(X) is the present value of Strike price.

This pricing equation ensure there is no arbitrage.

Let's take an example:

S = 100

X = 80

Risk free rate = 10%

T = 1 year

C = 25

Particulars	Amount
S	100.00
PV(X)	72.73
Net	27.27

It can be seen C (25) lies between the instrinsic value(20) and adjusted intinsic value (27.27).

Particulars	Amount
Buy the Call	-25.00
Sell Short the Stock	100.00
Invest on PV(X) at Rf	-72.73
Total	2.27

At Maturity Date,

Position	CF
S(after 1 year) <80	S(after 1 year) >80
Long Call	0	St - 80
Short Stock	-St	-St
Investment	80	80
Total	80 - St	0

We have enured that we had an inflow of $ 2.27 initially, with no arbitrage possibility later.