Explanation
Theta measures time decay, ie the change in value of the option with the passage of time. When the option is close to expiry, theta is very low as the value of the option is driven by intrinsic value rather than the time value. Therefore theta approaches zero as the option comes closer to expiry.

Explanation
An yield curve would be meaningless if it combines, for example, the yield on a AAA bond with the yield on a bond near default on the same curve. Therefore statement I is incorrect as any typical yield curve generally refers to similar instruments, and similarity includes similarity of issuer type and credit risk profiles.
Statement II accurately describes an yield curve, and statement IV explains what the term structure is.
Statement III is incorrect as the liquidity preference theory offers an explanation for an upward sloping yield curve and not a downward sloping one.

Explanation
Forward rates can be calculated from spot rates and interest rates using the formula Spot x (1+domestic interest rate)/(1+foreign interest rate), where the 'Spot' is expressed as a direct rate (ie as the number of domestic currency units one unit of the foreign currency can buy). In this case the forward rate will be 1.1239
* (1 + 0.75%*90/360) / (1 + 0.4%*90/360) = 1.1249.
It can be confusing to determine which interest rate should be considered 'domestic', and which 'foreign' for this formula. For that, look at the spot rate. Think of the spot rate as being x units of one currency equal to 1 unit of the other currency. In this case, think of the spot rate 1.1239 as "CAD 1.1239 = USD 1". The currency that has the "1" in it is the 'foreign' and the other one is 'domestic'.
It is also important to remember how exchange rates are generally quoted. Most exchange rates are quoted in terms of how many foreign currencies does USD 1 buy. Therefore, a rate of 99 for the JPY means that USD 1 is equal to JPY 99. These are called 'direct rates'. However, there are four major world currencies where the rate quote convention is the other way round - these are EUR, GBP, AUD and NZD. For these currencies, the FX quote implies how many US dollars can one unit of these currencies buy. So a quote of "1.1023" for the Euro means EUR 1 is equal to USD 1.1023 and not the other way round.

Explanation
All the choices listed are valid assumptions underlying the BSM option valuation formula except that the BSM formula is based upon the option being exercisable only at expiry. The assumption is that early exercise is not permitted. In other words, BSM applies to European options and not American options. Therefore Choice 'd' represents the correct answer as it is not an assumption underlying Black Scholes.

Explanation
For fixed income portfolios where standard cash flow discounting models are not available, duration calculations are based upon estimated price moves in response to a change in rates. Recall that we define duration as the percentage change in price expected for a 1% change in yield. In this case, we have three price points known to us:
Line | Price | Yield
a | $102 | r - 45bps
b | $100 | r
c | $ 97 | r + 45bps
(where r is the current yield)
The change in price from line a to line c is $102m - $97m = $5m. We use the middle point, ie $100m, to calculate the percentage change. Therefore the percentage change in price is $5m/$100m = 5%.
The change in yield between lines a and c is 90 basis points [=(r+45bps) - (r-45bps)]. In other words, the change in price is 5% for a 90 bps change in yield. So the duration can be calculated as 5/(90/100) = 5.56. The other answers are incorrect.