A short squeeze results when short sellers are trying to cover their short positions by buying in the spot markets, which do not have adequate supply. This results in sharp spikes in spot prices, which further forces any other shorts to try cut their losses. The result is a sharp rise in spot prices.

Choice 'a' is the correct answer, the other choices do not describe a short squeeze.

To solve this question, we need to revisit how delta is calculated in a single step binomial model:

Consider a portfolio with just two positions: 1 Long Call option, and Δ Short Stock. We do not know what Δ (Delta) is.

Now if the current price of the stock is P, which can take the value P2 (higher value) and P1 (lower value) in the future at time T, then Δ needs to be such that the value of the portfolio is equal in both the cases. If the price goes up, the value of the option will be $1 (given) and the value of the short stock will be -Δ P2. If the price goes down, the value of the option will be $0, and the value of the stock will be -Δ P1.

Therefore, $1 - Δ P2 = $0 - Δ P1.

Solving for Δ, we get Δ = $1 /(P2 - P1) = $1 / ($102-$98) = 1/4.

Delta hedges need to be rebalanced periodically because with changes in prices, delta changes, and the amount of hedge required changes as well, requiring a readjustment. The more frequent the rebalancing, the better the performance of the hedge. However, the greater the rebalancing frequency, the greater are the number of trades required, increasing the costs from trading. The trader has to balance transaction costs against the adverse effects from poorer hedge performance. Therefore rebalancing frequency is a consideration for a trader and statement I is true.

Statement II is not true. When options are granted, their future impact on the price gets priced in into the current price, and no change occurs when these are actually exercised.

Statement III is true. Consider the Black Scholes PDE

202.23.e1

and substitute delta = 0 (as this is a delta neutral portfolio), and we get the result 202.23.e. Since r is generally small, a large negative theta means a large positive gamma and vice-versa. Therefore theta can be used as a proxy for gamma and this statement is correct.

Statement IV is correct. Vega is highest closest to the strike price - look at the graph for vega to see how vega behaves with changes to spot. (Do it yourself or there is a graph in the tutorial too.)

To calculate the Modified Duration from Macaulay's duration, we use the relationship MD = D/(1+r), where MD is the modified duration and D the Macaulay Duration. Therefore Choice 'c' is the correct answer.

When hedging one fixed income security with another, the question as to how much of the hedge to buy (or sell) (ie the hedge ratio) for a given primary position is determined by their respective basis point values, which in turn are determined by their duration. Therefore, when hedging a long maturity bond with a PV01 of $3 with a short maturity bond that has a PV of $1, we will need to buy 3 times the notional value of the short maturity bond to achieve the same sensitivity to interest rates as the longer maturity bond.

Additionally, we may also expect the interest rates on the hedge to move differently from the interest rates on the primary instrument being hedged, and this needs to be accounted for as well as part of the hedge ratio calculation. This is called the yield beta and is calculated as change in yield for primary position/change in yield for the hedge security.

The hedge ratio is determined both by the yield beta and the BPVs of the two securities. Choice 'd' is the correct answer.

A CLN is a form of a funded credit derivative. The investors in the note are the protection sellers, and receive the CDS premiums in addition to any risk free rate on their investment. If a default occurs, the money put up by the investors in the CLN is used to make good the party that has brought the protection.

Therefore if a default occurs, the investors in a CLN do not receive their entire investment back, but only what remains after fullfilling their obligations on the credit protection, plus any premiums that might have been earned. In return for this risk, the CLN yields the risk free rate plus the CDS premiums. Only Choice 'd' is correct, all other options are incorrect.

Treasury bond futures do not specify which bond can be used to effect delivery, but allow the seller to pick from a number of available bonds. As a result, one of these eligible bonds emerges as being the 'cheapest' to deliver, and this CTD bond is determined by the basis between the cash price of the bond and the futures spot price as adjusted by the conversion factor for this specific bond. (ie, basis = Cash Price of the Bond - (Futures Price x Conversion Factor).)

The bond with the lowest basis is generally the CTD. In the given question, the three basis calculations are:

1) 97 - (0.9 x 105) = 2.5

2) 101 - (1 x 105) = -4

3) 106 - (1.1 x 105) = -9.5

Since the third bond with a quote of 106 has the lowest basis, Choice 'b' is the correct answer.

Over the counter and electronic communication networks match buyers and sellers. However, there is no market making function, ie, in periods of stress liquidity may completely disappear from these markets. Exchanges normally have market makers that are required to present two way quotes on the securities they are making the market for. Therefore Choice 'a' is the correct answer.

The underlying asset in a Treasury note futures contract is any long term Treasury note with a maturity of no less than 6.5 years and no more than 10 years. The underlying asset in a treasury bond futures contract is any long term US Treasury bond with a maturity of more than 15 years and not callable within 15 years.

Note the difference betwen what the underlying asset is for treasury bond futures and treasury note futures. In either case, adjustments will be made for the coupon and maturity of the actual bond delivered (the concept of the adjustment of 'cheapest-to-deliver').

This question is based upon a weather derivative contract traded on the CME in the US. For each day, 'Heating-Degree-Days' (HDD) is calculated as equal to 65 degrees Fahrenheit minus the daily average temperature. The daily average temperature is based upon the temperature reported by the Earth Satellite Corporation using a specified automated weather station. Based upon daily values of HDD, an aggregated number called the 'CME degree days index' is calculated for each contract month. In other words, the index for a particular month is just the aggregation of the 'HDD' value for each of the days of that month. Each contract settles at the end of the month at a value equal to $20 x Degree Days Index. (In a similar way, 'Cooling Degree Days' are also calculated and a futures contract offered, except that CDD is equal to the average daily temperature minus 65 degrees). (Source: CME's website at CMEGroup.com)

In the given question, we are interested in hedging against the possibility of the temperature being too low. This means we should buy the HDD futures contract (the lower the temperature, the higher the difference of the average temperature from 65 degrees, and the higher the settlement). Therefore Choice 'b' is the correct answer. The lower the actual temperature turns out to be, the higher the payout to the grower. It would not be wise to wait till January to buy the contract as by then the prices of the contract would have already risen if the grower's fears of a colder January appear to be coming true. He can hedge his exposure by immediately locking in the January prices.