## Interview Question: Option Application

Sample Question #257 (case question)

How can you model limit orders as a barrier option?

[A real interview question]
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### 3 Responses to Interview Question: Option Application

1. Brett says:

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.

2. Muting says:

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?

3. Liew says:

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.