In todays video we will learn about options on foreign exchange and index options.
Hi welcome back to my youtube channel so today we’re gonna learn about a few additional types of option pricing models and so really what we’re gonna look at is there’s options on a bunch of different underlines things like stock market indices things like like currencies things like futures and so we have slightly different models for pricing them and that’s
Just because of some of the core differences of those products so the first thing we’re going to talk about here are stock market indices so stock market index is a method of measuring the valuation movements of the basket of stock so they’re all things you’ve probably heard about we’ve got you know the dow jones index the s&p 500 the footsie the character
Dikes all of these different global indices that are essentially baskets of stocks now some indexes are a little bit different to others some are price indexes and some are total return indexes and so a price index is just the price performance of the underlying and the total return index includes reinvested dividend so obviously a total return index gives maybe
A more accurate description of the returns an investor would get if they bought all of the stocks in the index now some indexes are more suitable than others for for derivatives for early’s for being the underlying of a derivative now the reason for that is we’ll say something like the dow jones the dow was very popular in in the press you know it’s whenever you
Hear the markets up or down they’ll tell you however many hundred points the the down move that day now a lot of traders pay don’t pay a ton of attention to the dow they actually look at the sp500 the reason for that is because of how they’re weighted so the sp500 is a market cap weighted index meaning that the biggest companies have the biggest weight in the
Sp and the smallest companies are lightly weighted in the sp for the dow with its price weighted which probably made sense when it was formulated a long time ago but essentially how that what that means is do you just add up all of the price if you’ve got $40 stock of $50 to us so on you just add them all up and there they are weighted by the stock price now that
Doesn’t make a ton of sense because for example a small company could be heavier weight than another company and not only that every time there’s a stock’s let alone at the stocks all of the waiting’s gets readjusted so as you can imagine that’s quite complicated if you are trying to base derivatives on on that as an underlying so for that reason we traders usually
Look at this and p at least for american stock performance other types of indices so we’ve got like i said national indices like i just explained there’s things like sector indices that might look at things like the biotech sector the telecom sector the industrial sectors and and so on and the purpose of those sector indices they’re usually sub in the season for
Big index and they’re there just to give people an idea of how the various business components of the market are performing at a given time and then there’s all kinds of other indexes things like green indexes are ethical indices that will meet certain people’s ecological or social criteria so for example there are indices that will exclude tobacco and alcohol
And gun companies things like that that you know certain investors not want to put their money in so options of course exists on these indexes the global market for exchange traded stock market index options is huge it’s one of the biggest markets the bank for international settlements values at at three hundred and sixty eight thousand nine hundred million so
It’s it’s a massive market and the stock index option is the right but not the obligation to trade a given index at a given price by a given expiration date so that’s that’s all it is but it’s slightly different to to pricing an option on an on different paying underlying so we’ll have to look at that so uses of index options well one use is portfolio insurance
In fact basically the way we’re going to break down the uses is the way we do with all that derivatives we’re gonna just say that there’s speculators and hedgers so speculators are people who want to profit on predicting the direction of the given market or its volatility and portfolio insurance that is hedgers and that’s people who are buying put options on a
Given index in order to hedge a basket of stocks that they may own now that leads us to the idea of beta so in finance the beta of an investment is a measure of the risk arising from exposure to general market movements as opposed to idiosyncratic factors the factors that impact just a stock alone and so the market portfolio of all investable assets has a beta
Of exactly 1 a beta above 1 means that the asset is volatile and tends to move up and down with the market and so an example might be a big technology company that might be very volatile but also exposed to too market risk factors negative betas are possible for investments that tend to go down when the market goes up and vice versa so if a portfolio has a beta
Less than one we have to buy fewer options to insure it and if a portfolio has a beta above one we’re going to require more in the exceptions to hedge it and i have a video from earlier about calculating the hedge ratio for futures and it’s the exact same hedge ratio will be calculated for options so i’ll put a link to that video above ok so then as we know from
Our put-call parity slides the payoff of an insured portfolio so if the red line that you see on the screen right now is is the payoff of being long a stock market index our basket of stocks for example the blue line there is the insured portfolio and that’s where you’ve bought a put on that so your long the underlying longer put and that gives you the payoff of
Being long a call option which comes from put-call parity and if you want to learn more about that i have a video on that topic as well and so for options on indexes it’s reasonable to make the simplifying assumption the dividends are paid continuously and that the dividend amount is proportional to the level of the index so essentially we calculate a dividend
Yield so the dividend payment paid over the time period is modeled using the formula you see on the screen and then for some constant q which is the dividend yield we’re able to use the formula that you see on the screen right now it’s just a modified black scholes formula to price options on on an index so as you can see there it’s not a huge modification it’s
Kind of why in my in my class on the black-scholes model i pointed out how important the black-scholes model is because pretty much every model that’s come after it has really just been an improvement on a small modification but there haven’t been any massive breakthroughs since since the black-scholes model so that’s really it we just modify the black-scholes
Model slightly in order to price options on and indexer has a dividend yield so the next thing up our foreign exchange options and a foreign exchange option is a derivative where the owner is the right but not the obligation to exchange money denominated in one currency into another currency at a pre agreed-upon exchange rate by a specified date so once again
It’s it’s a standard option but instead of instead of buying stock for example we’re exchanging money from one currency into another until the black scholes model can once again be modified to price options on foreign exchange the modified formula is called the garmon called hagen model all of these formulas by the way are in my textbook which is called trading
And pricing financial derivatives and there is a linked about in the description below but the the garment called hagen model was developed in 1983 and it extended the black scholes model to cope with the presence of two interest rates so it’s a little bit like when we were pricing futures on foreign exchange we just have to deal with the fact that there is
More than one interest rate there there’s the domestic and the foreign interest rate so up on the screen right now you’ll see the formula for the garment kool hagen model and as you can see once again it’s a lot like the black and scholes model but we’ve got in there or d and or f or deeping the domestic risk-free simple interest rate and our f being the foreign
Risk-free simple interest rate so if you want to pause the video i’ll put the put the screenshot of the formula up so you can take a look at it maybe compared to the black-scholes mom so so that’s that’s really it that’s our pricing formulas now a few other things we’re going to talk about just kind of tidying up a few ends that we’ve left from our prior video
So one thing we’re thinking about with currency puts and calls is that a hood is a call and a call is a put in the foreign exchange world and that is because it really just depends upon which currency you’re thinking in in which country you’re denominated in as to whether you view yourself as buying or selling currency right because if your dollar denominated
And converting into pounds you would view it one way while if your pound denominated and converting from dollars into pounds you you would view it another way so foot is a call on a call as a pud and actually this you know with this foreign exchange stuff it actually really shows you almost the nature of put-call parity that the two you know the two options are
Extremely related to each other and so obviously the prices do have to be tied to each other so that’s really it honor are sort of wrap up on options pricing you know i’ll put a little write-up in the description below as well if you want to look at that that’s something i do with all of my videos so if you’re watching other videos and feel you need more detail
You know do look at the description below so you’ve you’ve made it over ten minutes into the video that means you have to hit the like button and if you want to see more videos like this if you find it useful please do subscribe and you can if you love love love the video want to hear you know every time i put a new one up you can hit the belt but now at the
Moment i’m uploading at a rate of you know a video a day so maybe you you don’t necessarily want to do that but you know what winds have gotten a lot of this stuff up i’ll probably move to a video a week at which point you know if you’re interested you might find that useful anyhow have a great day and i will see you again tomorrow with a new video bye
Transcribed from video
What are index options? What are currency options? By Patrick Boyle