Help with SIG Interview Question about Options

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DarkSkyParadise

Hey everyone -

I'm a rising senior interviewing with SIG for a full time TA position. A friend shared a pretty basic interview question he got on options and was looking for some help. The problem is this:

You have are offered a contract on a piece of land which is worth 1M 70% of the time, 500K 20% percent of the time and 150K 10% of the time. The contract says you can pay x dollars for someone to determine the land's value from where you can decide whether or not to pay 300K for the land. What is x? How much is this contract worth?

In college options courses, I've learned the basic tenets of options - the option price is not the discounted expected payoff of the option. Also, the probabilities of the underlying asset moving up or down are irrelevant to the stock price. But, here the interviewer gives the probabilities. Are the expecting me to determine the payoffs and take the expectation? Or should I constructing a replicating portfolio using the asset and cash and find the price that way?
 
Worth 529999.99

If your time is free. And you like to make a penny.

That's actually not a trivial question as the obvious answer is incorrect.



DarkSkyParadise said:
Hey everyone -

I'm a rising senior interviewing with SIG for a full time TA position. A friend shared a pretty basic interview question he got on options and was looking for some help. The problem is this:

You have are offered a contract on a piece of land which is worth 1M 70% of the time, 500K 20% percent of the time and 150K 10% of the time. The contract says you can pay x dollars for someone to determine the land's value from where you can decide whether or not to pay 300K for the land. What is x? How much is this contract worth?

In college options courses, I've learned the basic tenets of options - the option price is not the discounted expected payoff of the option. Also, the probabilities of the underlying asset moving up or down are irrelevant to the stock price. But, here the interviewer gives the probabilities. Are the expecting me to determine the payoffs and take the expectation? Or should I constructing a replicating portfolio using the asset and cash and find the price that way?
More...
 
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2rosy said:
How did you get this? Maybe i am coming up with the obvious solution 515
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I came up with that (or the full 815 prob value inclusive), too. It has to be wrong. It makes the 300K offer look silly low. We are solving based on cash flows which seem to be the right track, but I think the problem tests our basic understanding of optionality.

I find this vexing. In RL, an assessment if $250 bucks.
 
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Its similar to the dice problem that they have been known to ask. You roll a die and get the payout (if you roll a six, you get $6, if you roll at 2, you get $2). How much are you willing to pay for this contract? The follow up is, how much are you willing to pay up front) for the option of rolling again?
 
newwurldmn said:
Its similar to the dice problem that they have been known to ask. You roll a die and get the payout (if you roll a six, you get $6, if you roll at 2, you get $2). How much are you willing to pay for this contract? The follow up is, how much are you willing to pay up front) for the option of rolling again?
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  • $3.00 for each contract/roll
  • Maximum loss $2.00
  • Maximum gain $3.00
  • Risk:Reward 2:3


:)
 
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