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Today we will learn about pricing financial futures

Today’s video is part two of pricing financial futures make sure you check out part one first to understand how our basic formula for pricing futures works and in that video i tried to explain the intuition behind the formula so rather than me just telling you a formula which you can obviously just google i try to walk you through why it makes sense um if you’re

New to derivatives take a look at my other videos explaining what derivatives are what futures are so on and so forth i’m do subscribe to the channel as well i’m constantly putting up more finance videos with the goal of taking finance students from a beginner level all the way through to an advanced level of understanding these videos are all based on my book

Which is called trading and pricing financial derivatives and it’s available on amazon.com so if you’re really interested in the topic you might be worth taking a look at that it’s also available in lots of libraries so i’ll put a link in the description below to amazon.com and you can check it out if you want to ok so let’s dig into today’s topic which is

Pricing futures exceptions to the basic futures pricing formula so in a perfect market the relationships between futures and the spot price or the price of dan they’re lying depends 100% on the formula which is showing on your screen right now and i explained that in the last video i also explained in the last video that there are some real-world issues such as

Transaction costs different borrowing and lending rates restrictions on short selling and so on that will prevent perfect arbitrage thus the futures price varies with in arbitrage boundaries of theoretical price in certain cases we need to make some small modifications to the basic formula in order to take things into account things like storage costs dividends

Foreign currencies that sort of thing when the underlying has a cash flow associated with it we need to take this into account in our formula the cash flow might be an interest rate on a bond or a dividend on the stock accumulated dividends on an index things like that so what we’re gonna do is we’re gonna use the letter q to denote the percentage cash flow on

The underlying asset and the formula can then just be modified into the following formula f0r the fair value of our future or forward right now at time zero whenever we’ve got a zero it’s at time zero which means right now so f 0 equals s 0 which is the price of the underlying right now at time 0 times e which is euler’s number that we covered in the last video

To the or minus q interest rate or as interest rate less cash flow as a percentage to the t which is the time remaining until expiration so as you can see we just needed to make a small modification to our formula in order to price a future or forward that has a cash flow associated with it next let’s look at how we deal with storage costs some underlyings have

Storage costs associated with them this is often the case with physical commodities things like oil or gold if you buy physical gold as an investment you usually don’t just keep it in a pile in your apartment your friends might be lovely people but there is a risk that when you invite them around for dinner every time you leave they’re gonna fill their pockets

Up with your your pile of gold coins and so usually what you’re going to do is you’re going to pay some sort of a fee to store it equally with things like oil you know your your neighbors would complain because you’ve got a thousand barrels of crude oil stored in a shed in your back garden and so once again when you own crude oil as an investment you usually

Will have to pay some sort of a storage cost and when there is a cost like this a known cost we need to obviously take this into account when pricing our futures so you can hopefully already guess how we’re going to deal with this because a storage cost is a lot like the cash flow that we spoke about a moment ago but rather than being a positive cash flow it’s

A negative cash flow it’s a cost rather than an interest amount that you’re earning and so where you is the percentage storage cost on an underlying the formula is f 0 or the fair value of our future our forward right now at time 0 equals s 0 are the price of the underlying also known as the spot price in the market right now at time 0 times e which is euler’s

Number to the or plus you interest rate plus storage costs as a percentage to the t which is the time remaining until expiration so next up how do we find the fair value of a foreign currency future when we’re dealing with foreign currencies there are two interest rates that we’re looking at this the local interest rate or the domestic interest rate is is often

Called and then there’s the foreign currency interest rate luckily we’re able to work around this quite easily with it once again a small modification to our original formula the formula for foreign currency futures is f 0 which is a fair value of our future now at time zero equals s0 or the price of the underlying in the market right now at time zero times e

Which is euler’s number to the r minus rf which is local interest rate minus the foreign currency interest rate to the t which is the time remaining until the contract expires so all of those formula hopefully makes sense to you in our next video we’re going to look at convenience yield but we’ll we’ll have a separate video for that you will need a financial

Calculator to calculate all of the above formulas and a lot of the formulas that we’ll cover in other videos i’ve put links in the description below to the two that are used on the cfa exams as a lot of people like to use those ones they’re both quite similar so do read the amazon refused before you decide which one appeals to you hopefully you found this video

Helpful please hit the like button below tell your friends who are interested in these videos and make sure that you subscribe if you’d like to see more content like this also please do comment below let me know about you about why you find these videos interesting and let me know if there’s any other financial topics that you’d like me to cover i plan on making

Lots of these videos then you have a great day see you again soon bye

Transcribed from video

Pricing Financial Futures (Part 2 of 2) By Patrick Boyle