Let me explain the two concepts:
Limit order: a limit order is an instruction to buy or sell some asset (e.g., shares of a stock) at some specific price. For example, a limit order to buy 100 shares of MSFT at $34 means the order should be executed only when MSFT trades at $34; the order will not be executed when MSFT is above $34. In other words, a pre-determined "barrier" (the limit price) must be broken before the order is executed in the marketplace.
Barrier option: aka a knockout option, a barrier option requires the underlying asset’s price to cross or reach a given level before it can be exercised, regardless of whether the option itself is in-the-money or out-of-the-money.
My attempted answer: For buy limit order, it is a down-and-in call. For sell limit order, it is a up-and-in put. The thing I dont understand is limit order is like an obligation once we hit the limit, but the barrier option is still a right rather than an obligation. How to model this part?
My attempt, only approximate answer:Assuming the buy limit order is $34. This is almost equivalent to a Down-and-in call with both strike price and knock-out price $34.Scenarios, path for stock price, S:1) S > $34 all time (Buy limit order not carried out, option expires worthless)2) S touched $34 and went back up (Buy order executed at $34; option is exercised to purchase the stock at maturity)3) S crossed $34 and went all the way down (Buy order still executed at $34; option expired worthless, but the option holder can now buy the stock for price cheaper than $34!) Scenario 1 and 3 is equivalent to the buy-limit-order whereas 2) is not. If we were to model the buy-limit-order as a product, it should be cheaper than the down-and-in call.
Fill in your details below or click an icon to log in:
You are commenting using your WordPress.com account. ( Log Out / Change )
You are commenting using your Twitter account. ( Log Out / Change )
You are commenting using your Facebook account. ( Log Out / Change )
You are commenting using your Google+ account. ( Log Out / Change )
Connecting to %s
Notify me of new comments via email.
Notify me of new posts via email.