Okay, so the question of the day that threw me off was Schweser challenge #15, reading 62 - options markets. The question asked for the value of an American option on a two-year bond with a strike at par. Basically after one year, you would want to exercise the option in either the up or down case, because both would yield higher values than the option value going forward. The end result was something like a value of $2.20. But at t=0 the bond was worth $106. So what I don’t understand is why wouldn’t you exercise the option immediately, and collect the $6 spread over par? American options can be executed at any time, right? I would think that should include the t=0 case. Any ideas?
What’s the interest rate? I don’t have the question, but an initial blind guess says that it may not be optimal to do so. You have to consider the fact that it costs money to buy it now with borrowed funds, and hold it for that time period.
Here’s the problem: An analyst has calculated the value of a 2-year European call option to be $0.80. The strike price on the option is $100 and the underlying asset is a 7% annual coupon bond with three years to maturity. The two-period binomial tree for the European option is shown below: t=0 t=1 t=2 Int. rate=8.56 price=98.56 option value $0 Int rate 5.99 Bond price 100.57 Int rate 3.00 ^ option val 0.29 Int rate 6.34 price $106.00 price 100.62 option val $0.8 option val. $0.62 Int rate 4.44 price 103.80 option val 1.35 Int rate 4.70 price 102.20 option value 2.20 The value of the comparable 2-year American call option with a strike price of 100 is closest to: A. 1.56 B. 2.12 C. 3.80 Okay, so fine, I understand how to get $2.12, but why is the call value not $6. I mean otherwise I buy the call today for $2.12, I exercise immediately and buy a $106 bond for $100 and collect $3.78 in arbitrage profits. The call value can’t be less than the current price of the bond less strike for an American option, can it? Hopefully someone can help cause that took me way too long to recreate…
Damnit. Stupid tree didn’t post properly.
Let’s try dis: t=0---------------------- t=1 -------------------t=2 ---------------------------------------------------------Int. rate=8.56 ----------------------------------------------------------price=98.56 -----------------------------------------------------------option value $0 ----------------------------Int rate 5.99 -----------------------------Bond price 100.57 Int rate 3.00 ^ --------option val 0.29 --------Int rate 6.34 price $106.00 -------------------------------------price 100.62 option val $0.8 -----------------------------------option val. $0.62 ----------------------------Int rate 4.44 ----------------------------price 103.80 ----------------------------option val 1.35---------- Int rate 4.70 ----------------------------------------------------------price 102.20 ----------------------------------------------------------option value 2.20
Ok. In this case, disregard my post above. It appears to me to be a bad question. I have tried hard to come up with a reason why the answer is not $6, and cannot.
Maybe you just can’t exercise the option in T=0?
where is this question from? I doubt they will ask you to calculate the value of an American option as it entails far more work and time. I think it will be a European-style option that can only be exercised at expiration on the exam. For American, you could exercise at any point, but it may be useful to know that for American calls, its never optimal to exercise before, so you could treat as European. Good thing Asian options aren’t covered in the curriculum. 
is this qbank? what is the q #. no way that is priced at 106 in t = 0. no way. that is the weird looking thing here- the $106 isn’t right. you sure that’s what they give you as t=0’s px? i seriously doubt it.
This is one of the challenge problems in qbank. If I remember correctly, Schweser states on the text of the chapter that that problem was included so we can go through the exercise of valuing an American option - but it is not something we would have to do on the test. Just remember that an American option will be worth more than a European option because of the optionality of exercising early unlike European options.
mp2438 Wrote: ------------------------------------------------------- > For American, you could exercise at any point, but > it may be useful to know that for American calls, > its never optimal to exercise before, so you could > treat as European. > this statement is true for american calls written on an underlying non-dividend paying stock that is assumed to be lognormally distributed. it is not true in general, it is not even true for dividend-paying stocks, and it is not true here in particular since the underlying is a coupon-paying bond whose price evolution is not the same as that of a stock
bannisja Wrote: ------------------------------------------------------- > is this qbank? what is the q #. no way that is > priced at 106 in t = 0. no way. that is the > weird looking thing here- the $106 isn’t right. > you sure that’s what they give you as t=0’s px? i > seriously doubt it. the bond tree is constructed fine - why do you think the $106 is weird. One period ahead you can sell the bond for $100.57 or $100.38 - expected value is 1/2*($100.57 + $100.38)=$102.185. You can also collect a $7 coupon payment - $102.185+$7.0=$109.185. Discount this back at the forward one-period interest rate of 3%: $109.185/(1+3%)=$106.0 the problem is misspecified because it assumes that you can’t exercise the american call at t=0. the option value should be at least $6
Looking from an arbitrageur perspective, there’s a flat $3.78 risk-less profit if the bond is not under the call protection period today (t=0)
I agree with jankynoname. He/She has a point here. From the interest rate tree, the bond price (given) is $106 at T=0. If the strike price is $100, value of American call should be $6. Very resonable.