Options pricing model

[FRED]

Anyone have a link to the above.

Normally a goggle search will provide but is now dominated by for sale products.

Cheers.

FRED

[zyreon]

email me and I'll send you a basic excel file for black scholes

[winner69]

A great place is here
http://www.hoadley.net/options/calculators.htm

Just click on the picture of the type you want to use

Have a good play .... good stuff

[Shrewd Crude]

Hey Fred...on NZO page 792 I have done an example of the Binomial Options pricing model, if you havnt seen it... valuing of a call option example ... It is different from the link winner gave, and all other Black Scholes examples in that it it doesnt use volatility..
you cannot get an accurate answer using a guess on volatility, try two different estimates (guesses), of this and you get completely different values...

In the BOPM the idea is too create a perfect hedge... this is done by two end of period payments which are always equal.... you then discount this figure to a present value using the risk free interest rate... with a hedged portfolio the shareprice doesnt affect the investors payoff.. so risk and return parameters such as standard deviation, variance, Beta, volatility, dont matter...
small virations of BOPM are used by some major financial firms...

Black Scholes is overrated, especially if you are new to the whole options thing kind of like me... start with a simplier model like the one I have shown.... just substitute your own values in...

[blackcap]

quote:Originally posted by Shrewd Crude

Hey Fred...on NZO page 792 I have done an example of the Binomial Options pricing model, if you havnt seen it... valuing of a call option example ... It is different from the link winner gave, and all other Black Scholes examples in that it it doesnt use volatility..
you cannot get an accurate answer using a guess on volatility, try two different estimates (guesses), of this and you get completely different values...

In the BOPM the idea is too create a perfect hedge... this is done by two end of period payments which are always equal.... you then discount this figure to a present value using the risk free interest rate... with a hedged portfolio the shareprice doesnt affect the investors payoff.. so risk and return parameters such as standard deviation, variance, Beta, volatility, dont matter...
small virations of BOPM are used by some major financial firms...

Black Scholes is overrated, especially if you are new to the whole options thing kind of like me... start with a simplier model like the one I have shown.... just substitute your own values in...








Shrewdie, buddy, the binomial is the same as the Black Sholes, or accurately a derivative of.

What do you think Share price UP and Share price Down in effect constitutes...... yep, volatility. BUt in effect it is the same model based on the same events.

Ok you dont have to pyhsically work out SD but in effect you are doing that but having an upper and a lower limit.

[Shrewd Crude]

hey Blackcap
the limitations of black Scholes are
#1- stock paying no dividends, until after expiration date
#2-interest rate, variance of the stock are constant, predictable .... (in what world are interest rates predictable?)
#3-no extreme jumps in stock price, eg takeover attempts ruleout this model , (obviously this model was not created for NOGGERS, huh!)

variations on the Black Scholes such as the Binomial Model were designed to deal with some of these limitations...
to me these models are much different, but also similar in some ways... #3 must make B/S and BOPM different on some level...

again.... in the BOPM we have created the perfect hedge... with two end of period payments which are identical... to find the value of the option in terms of the stock we therefore do not use volatility as a measure...
yes volatility is present in the picking of the two stocks but thats it, it is not measured in BOPM... it is not used in any BOPM formula such as it is in B/S.....

Is anyone having problems working out the standard deviation for B/S...?

anyway, The blackcaps are my favourite team.... did u know that Stephen Fleming is my fathers name.... and not the same dude that posts on this site either...

[FRED]

Thanks guys.

One model I have found has an input(default 50) for binomial of steps.

What is this? The range over x period? High minnus low?

FRED

[Shrewd Crude]

Put-Call parity.... this equation can be used to calculate the value a call option, put option, share price.... mispricing in the model can create the asutue investor risk free profits

c + Xe^(-rt) = p + S

c= european call option
p=european put option
S= Share price
X=exercise price of call and put option which equal...and exerciseable on the same date...
e=2.71828........
r= risk free rate
t=time (in years)

for this model to work, the call and put option strike price must be the same... this model works well with American shares where all large companies, and smaller stocks too have put and call options listed... NZ stocks don't have put options because we have an illiquid market, some auzzie stocks may?

in this equation if both sides equal then there are no arbitrage opportunities.... if they are different then you can make risk-free profits...
This equation is good because you can find out the value of a Put or a call, or a share price if you have all the other info and no arbitrage theory holds...( you can use change of subject to make the whole equation equal to say a put)
eg c + Xe^(-rt) = p + s
p= c + Xe^(-rt) -s
so you don't need the value of the put, just all the other info!

[8D]
.^sc

[Shrewd Crude]

lets look at an example......
S=$31
X=$30
r=.1 ........ risk free rate
t=3 months ......... time
c=$3
p=$2.25

so, c+X(^-rt) = $3 + 30/(1.1^(3/12))
=$3+$29.29 = $32.29

p+s= $2.25 + $31= 33.25

the two equations don't eqaual, so arbitrage profits can be made.... we sell the share and the put because it is more expensive and buy the call
....so buy the call, short the put (sell), short the stock...
this leads to an initial cashflow of 31-3+2.25=30.25
invest this for 3 months at the risk free rate... 30.25*.1=3.025
3.025* (3/12)=.75625 ....... .75625+30.25=$31.01

or 30.25 e^(.1*(3/12)....

at the end of the 3 months the possible situations are as follows...
1. stock price is greater than $30, so the investor exercises the call... this involves buying a share at $30... The short position is closed out and the netprofit is $31.01-$30=$1.01

2. Stock price is less than $30. The counterparty exercises the put. This involves the investor buying one share for $30. short position is closed out and the net profit it
31.01 - 30= $1.01

If there are dividends then the equation becomes.
c + D + Xe^(-rt) =p + s
[8D]
.^sc