Replicate digital option call spread
When a new trade comes to the risk manager in a bank for approval, he tries to replicate digital option call spread both the quality and the quantity of the risks inherent in the trade. If he's not comfortable with either of the two, he may not approve it.
Some of the factors that are considered are: Whether the bank has a model to price and determine the risk of the trade. And yes it happens, with virtually any payoff possible in the OTC equity derivatives markets, the bank will not always have the model to handle the trade. Number of underliers to the trade and whether these underliers are liquid indices or thinly traded stocks.
Managing replicate digital option call spread risks of a multi asset trade with illiquid stocks as undeliers would be the most difficult. Discontinuities replicate digital option call spread the payoff. The greeks-delta and gamma in general as the spot approaches the barrier become extremely volatile. Ofcourse, Not all trades require pre approval esp. For new payoffs the trader will come up wth an overall hedging strategy for the trade. Often the most important aspects of the hedging strategy revolves around managing greeks around discontinuities or barriers.
In this article, I shall talk about 'Overhedging' which is a technique to handle effectively risks around barriers. What the trader achieves by doing so is a smoother set of greeks specially the delta.
As an example let's consider a binary option in the figure below booked as a call spread. It's important to note that the call spread is structured that it is more expensive than the original binary option. What this means is that when a buyer comes to a bank with a price request for a digital option, the bank actually quotes price for a call spread.
To extend the discussion to the barrier trades, a barrier trade can be viewed as a combination of an option spread and an replicate digital option call spread. For example an up and in call option can be booked and replicate digital option call spread as a combination of a call spread with strikes being barrier and barrier - overdhedge and a call option with strike equal to the barrier level.
A physicist thinks reality is an approximation to his equations. A mathematician doesn't care. Managing risks of Digital payoffs - Overhedging 3.
I have my own problems to solve. I'm never likely to go there. I am just short the profit at the moment.
This post is based on problems 2. I was asked how to price a digital option in a job interview - and had no idea what to do! A call is only worth exercising using if the underlying price,is greater than atas the payoff from exercising is.
A digital call option with replicate digital option call spread similar - it replicate digital option call spread off one dollar if at expiration, and pays off zero otherwise:. Suppose you have a model for pricing regular call options. How can you use to price the digital option? As a starting point, consider buying a call with and selling a call with:.
This is close to the digital option, but not exactly right. We want to make the slope at steeper, so we need to buy more options. Consider buying two calls with and selling two calls at:.
As opposed to a slope of 1 between andnow we have a slope of two between and Generalizing this idea - consider a number. To get a slope replicate digital option call spreadyou buy calls at and you sell calls at.
How much will the above portfolio cost? You earn from selling the calls, and pay for the calls. The net cost is: Many complicated payoffs can be re-created as combinations of vanilla puts and calls. Digital Call Options A replicate digital option call spread call option with is similar - it pays off one dollar if at expiration, and pays off zero otherwise: As a starting point, consider buying a call with and selling a call with: Consider buying two calls with and selling two calls at: Given that the slope isto get an infinite slope, we take the limit as goes to zero.
It might look more familiar if I re-wrote it as: Conclusion Many complicated payoffs can be re-created as combinations of vanilla puts and calls.
Several meetings have also happened between Madhya Pradesh and Rajasthan about the Replicate digital option call spread link mentioned above.
The Government of India has prioritized this link, but by taking up this project unilaterally without consent of Rajasthan or Centre (Ministry of Water Resources) the Madhya Pradesh government is violating the interstate and federal norms. The EIA does not even mention any of these issues.