How to Price Exotic Options in R - YouTube

Hi, everyone! . In this video, we are going through the option pricing by using R program

How to price options?

Well, options are priced depending on 6 parameters, as follow..

The current price of the underlying asset; S

The strike price; K

The underlying asset’s volatility; sigma

The risk-free rate; r

The dividend rate; q

the formula here, there is already subtract with the risk-free rate, so it show only “r” here

And the time-to-maturity with units in years; T

The function N() that appears in the formula, denotes the cumulative function of the standard normal distribution.

However, there are assumptions behind the model.

Obviously, these assumptions do not meet in reality,

but the black-scholes model offers you the best way to price options for now.

Now, let’s price an option by using this Black Scholes model in R

Before we start, just so you know,

we’ll be focusing on the option pricing functions only.

For other purposes, you can take a look online.

First, we open R studio program, there are actually 4 main parts

Top Left is for writing commands

Bottom left is result of submitting the codes that you wrote

Top right shows the environment and Bottom right shows plots

You can type your code as a function here

I will give you an example of the general option price model that we’re all familiar with

-- BlackSholesMerton, which the model is the closed form formula to price an option.

Let’s say I would like to compute a call option price

given 6 variables spot price s, strike price k,

annual risk free rate r, volatility sigma, dividend yield delta,

time at maturity double capital t, time at evaluation double small t

First we need to state 6 inputs in a function of BSMCall,

then, open the blanket to input d1 and d2 formulas

After we state that d1 and d2 are normal distributed function,

then state call option pricing formula, I named it as “callvalue”

CallVal = S*exp(-delta*(TT-tt))*pnorm(d1)-K*exp(-r*(TT-tt))*pnorm(d2) which is the formula above, close the blanket.

After we finish filling formula, we then compute by giving 6 inputs

Call1=BSMCall(spot = 96, strike price = 90, annual risk free rate = 0.1,

sigma = 0.25, delta = 0, Double capital t=1, double small t = 0.25

Lets run it!

There is an error. It says “unexpected close blanket” here,

so we can go back, check and delete our error.

Okay! after we fix the mistake, run it again.

The result is the call price based on input 6 variables is 15.5

As you may know, there are different variety of options out there in the market.

Depending on benefits and cost of risk,

we can generally categorize into standard option and exotic option

Let's share 3 types of exotic options

to get you familiar for your future studies:

Asian Option, Binary Option and Lookback Option.

Ok! Let’s get started with Asian Option.

The reason I pick Asian Option first is because

his is a basic form of exotic options.

Its payoff is pretty much similar to standard options.

The difference is that payout is determined by the average value of underlying asset over predetermined period.

whereas, payoff of standard options depends on price of underlying at specific point in time.

Therefore, it is also known as “average value option”.

Basically, these options allow you to buy or sell the underlying at the average price instead of spot price.

After we have done manually priced a call option using Black Scholes model,

I prepare the package of codes that contain 3 main pricing commands for each exotic option.

But first, you need to download the file “FExoticOption”,

then we need to install the file from our library using this command.

After we install the file, Asian option’s formula in R is called GeometricAverageRateOption.

If you have no idea what GeometricAverageRateOption is, you can simply fill “?” sign in the front.

Then, you highlight and run the code.

The bottom right pop up information of GeometricAverageRateOption for you. Easy-peasy right?

Are you following us? I hope yes. Now! let’s tell R the value of your 6 variables!!

I apply the previous example from the Black Scholes model which

spot price is 96, strike price 90. Time is computed from 1-0.25 which is 0.75, r = 0.1, delta b = 0.1, sigma = 0.25

Noted that type flag C means that I would like to price call option.

Are you ready? check your codes, then run! Here you go!

Price1 is the CALL option price. You can click it for more detail to see input parameters and the value of this call option which is 9.96.

But if you want the price to immediately pop up on the screen, you just add one more command at the back which is @price

Then why we use this option? Due to its features,

its volatility is less than the volatility of the spot price which make asian options are less expensive than standard counterparts.

It can also reduce the market manipulation which is another main benefit.

On the other side, Asian option will not provide the opportunity to make large profit at peek moments which is created by high volatility.

Wake up!!!!!!!!!! We are moving onto the second exotic option: Binary Option

As you may aware of the name “binary”, this option simply depends on either of the two outcomes

which is a “yes or no” proposition.

You will get the payout if option expires “in the money” and incur a loss if it expires “out of the money”.

The main features of binary option are a fixed maximum payout and it limits the risk only for the amount that you invested.

So, you don’t have to bother with the price movement of underlying.

No matter which types of binary option you trade,

the risk is the “position size” on a single trade.

Binary option pricing for R is pretty much similar to Asian option in terms of input variables.

I brought you 2 examples, one is “Asset-Or-Nothing-Option”, and another is “Cash-Or-Nothing-Option”.

Inputs of “Asset-Or-Nothing-Option” are similar to Asian and European options,

So, here is the example for you, TypeFlag = "p" for put,

S = 70, strike price X = 65, Time = 0.5, r = 0.07, b = 0.02, sigma = 0.27.

But for “Cash-Or-Nothing-Option”, one additional variable is required which K is the cash at the expiration

if the binary option is “in the money”. The command is

“CashOrNothingOption” (TypeFlag = "p", S = 100, X = 80, K = 10, Time = 9/12, r = 0.06, b = 0, sigma = 0.35)@price

There you go the prices of both binary options are shown, and I will leave binary-barrier options for you to try!

Here we come to the last exotic option for this video, the Lookback options.

Again, for more details you can search online.

To price the lookback option,

we calculate the option's price at or near the widest expected distance of price differential,

based on past volatility, and demand for the options. There are 2 broadly types of Lookback options...

Firstly, the floating strike lookback option,

we calculate the payoff by comparing the closing price and the most favorable strike price.

So, the input variables of floating strike lookback option are similar to Asian option.

The lowest price is observed from the underlying in the case of the call

or the highest price in the case of the put (SMinOrMax), instead of strike price.

You can simply compute the price in R. For example, you want to price a call option with the current asset price at 120 dollars.

The asset used to have the lowest price at 100 dollars.

The contract will be expired in 6 months. The risk-free rate is 1%. 5% is cost of carrying, and 30% for volatility.

Then bang! The price of this options would be 27 dollar as shown here.

Secondly, fixed strike lookback option, we fixed the strike price as always,

but the holders can pick the best underlying asset price to compute the payoff.

Pricing this option is the same as the floating strike lookback option,

but we need one more factor, which is “the fixed strike price”.

Let’s assume that the fixed strike price is 110 dollars.

We type the formula, add the same variables as previous and add the strike price here…

Then, we run the result.

So, the price for fixed strike lookback option would be around 35 dollars.

Here we come to the end, we do appreciate to make this VDO and thank you everyone for watching.

You can find our coding package under this VDO. Thank you so much