Barrier exotic options explained: knock-in and knock-out (Excel) transcript

hi everyone and welcome again to nettle we go to a place to learn about business finance economics and much much more please don't forget subscribe to our channel and click that bell notification button below so that you never miss fresh videos and tutorials you might be interested in many thanks to our current patreon supporters and youtube members for making this video possible and would also greatly appreciate if you consider supporting us as well so please check the link in the description and click the join button below for more details my name is sava and today we're investigating a very common type of exotic options there is barrier options and will investigate both knock in and knock out calls and puts learn how to calculate their payoff structure and how to visualize those in a graph many thanks to stephen huntley for suggesting this topic for this video so let's start the barrier options overall are an exotic type of options it means that they are more complicated contracts than your vanilla options and they can be uh knock in and knock out in terms of some barrier price age h stands for hurdle and that is a price that shapes the payoff structure of barrier options additionally to the strike price and the premium the barrier price is a level that the underlying price must cross for the option to become active or inactive if we're talking about knock in and knock out options respectively so for example calls can be up and in and up and out an up and in call option would be inactive unless the underlying price during the lifetime of the option contract does not reach the barrier price age whereas an up and out call option would remain active unless the barrier price h is reached over the lifetime of the option contract whereas for puts there is a direct analogy with down and in and down and out down and in puts would remain inactive unless the barrier price h is reached so if the underlying does fall at or below the barrier it would become active whereas the down and out would be a knockout option and it would cease to be active it would become inactive if the barrier is reached for the sake of simplicity let's model center price knock in and knock out options so for example let's say that our strike would be a hundred dollars per share for example for all four of our options that we seek to model today all options would have a premium of five and the barrier would be 115 for calls it's again very typical and very logical for barrier calls to have a barrier price that exceeds the strike whereas for the ports it is quite conventional to have a barrier price that is below the strike for example 85 then we can model a range of underlying prices that will strive to calculate the payoffs of our barrier options for and let's use the sequence function to simplify that and for barrier options modeling so that the graphs look prettier we need to preserve a quite high level of granularity so let's go for 501 rows in one column we just need one column of underlying prices and that means that we'll have to simulate the prices from 75 dollars per share with a step of uh 10 cents per share 0.1 dollars per share which would bring us from 75 up to 125 with 100 being right at the center being our center price quite naturally so for an up and in call we would first of all subtract the premium that's something that as in case of uh vanilla options conventional options we pay regardless of the outcome again we are modeling long contracts here short contracts would be exactly the reverse and then we need to add the typical long call payoff structure which is the maximum of zero and the difference between the underlying price that we need to lock the column for but not the row minus the strike price and here again the financial implications of it are quite simple as uh the call option uh gives us an opportunity but not the obligation to buy at the strike we would exercise our call if the underlying price is in access of the strike if the option is out of the money and gain the profit which is the difference between the underlying price and the strike will basically buy the strike and sell at the market price however in case of the barrier options we would only be able to exercise that if the option remains active for the up and in call option we would have this opportunity if the underlying price is at or above the barrier meaning that we have to multiply it by the if function and if would be well the underlying price is at or above so great or equal to the barrier again lock in the row for a barrier and the column for the underlying price if that's the case then one and zero otherwise then we can enforce display of structure throughout the range of our underlying prices and here at the graph we would have the payoff structure for the up and in call unlike the conventional vanilla call option that would have an increasing payoff structure throughout the out of the money uh the up and in call kicks in only when the underline is above the barrier price h so our player structure is flat and negative we just lose the premium all the way until the price is 115 which is our barrier and if the barrier price is reached and exceeded we gain um ever and ever increasing upside just in case of the regular long call so here we see that the up and in call is quite a bit less valuable than the conventional loan call given that you would have upside over here for your conventional loan call however that would be a little bit cheaper in terms of the premium and that gives you exposure to this particular payoff structure which conventional options do not allow you to get and again that's the main idea of financial engineering in general and exotic options in particular that those are designed to give you exposure to payoff structures that other instruments do not provide in terms of the up and out call we can drag this formula across and modify it so that the new logic the new logic of the knock out barrier option is preserved and here the only thing that we need to change is that the option would be inactive if the barrier is reached or exceeded and active if it's not and let's see how it affects the payoff structure for the up and out call the payoff structures uh to some extent the reverse we do gain the conventional long call exposure but only until the underline reaches 115 at 115 the option ceases to be active and we continue to just lose the premium if the share price is in access of that and that can be nicely corresponded to various uh forecasts that an option trader might have for an up and in call the trader as we see from the payer structure from the exposure is extremely bullish they are willing to forgo the upside if the share price just moderately increases for the exchange of a tremendous upside if the share price is uh ahead of the barrier whereas for the up and out call the trader is little bit less uh bullish is a little bit less high volatility as here we see that the trader is willing to accept the upside only if the share price is uh well between 100 and 515 that's the only range of prices when the trader breaks even and gains positive profits and what is also quite neat for those two options is that we add if we add those two together we would get exactly the payoff structure of a conventional uh long call and that is something that is handy for valuation purposes that is perhaps something that we're going to investigate in one of the further videos if you are interested in barrier options and some of the more detailed specificities now we just need to move on to our put contracts and for the down and input we can copy this particular formula around and change uh the formula so that reflects the logic of a down and input first of all the source of the upside for the port is the reverse difference it's the difference between the strike and the underlying price simply because the long put gives you an opportunity but not the obligation to sell at the strike so if the option is in the money if the underlying price is below the strike you can buy at the market and sell at the strike and the only other difference that we need to take into account is when this option becomes active so the option becomes active if and only if the underlying price goes at or below the barrier so here we just change this formula to lesser than or equal to and that corresponds to the down and in put payoff structure with flat downside equal to the premium if the share price is above the barrier but the option kicks in at a very high payoff when the share price is at or below the barrier the hurdle price of 85. and again this strategy can be considered as very high volatility barrier strategy as you're willing to forgo the upside if the share price is between 85 and 100 for a higher upside if the share price goes further down below the barrier of 85 and the idea is that obviously the down and input would be cheaper in terms of premium than the conventional uh long put with no barriers involved finally for the down and output we can copy this formula and change the conditions here so that the option becomes inactive when the huddle the barrier price of 85 is reached or broken through and that visualizes the payoff structure with increasing upside if the share price goes further further down up until 85 when the option ceases to be active when it becomes inactive and the payoff structure remains flat at negative 5 ever since one of the other considerations that you need to take into account when modeling these options is that they depend on the path the price go through before maturity even if those barrier options are european even if you can exercise them only at maturity they would become active or inactive depending on where the price goes throughout the contract period because for example if the down and in put is held and the share price falls to 80 but later on goes up to 90 the option still is active however the uh payoff that you'll get would be smaller this is something that those payoff charts cannot adequately represent and that's why we need when modeling evaluating or pricing these options to simulate or take into account analytically the path the share price can uh take throughout the lifetime of the option contract and that's all there is for the basics and visualizations of barrier options including both knock in and knock out options that is up and in call down and input up and out call and down and out put please leave a like on this video you found helpful in the comments below i make to see any further suggestions for videos in business finance or economics topics you'd like me to record and please don't forget to subscribe to our channel and support us on patreon thank you very much and stay tuned