CT8 2011 09 Q9 (iii) and 11(iii)

[Helloall]

Hi,

I was wondering if you could help me to understand these two questions.

9(iii). I always seem to get the values of shares/cash with the opposite signs. If I want to hedge a call option do I not want to have -2600 shares, this will give me a negative delta which will cancel the call option delta? Why is it positive in the solutions?

11(iii) I thought I could follow this simple equation of calculating the probabilities of transition:

Prob = 1 – exp(-Lambda).

where lambda represents the transition intensity.

However, when I use this equation to build up a solution I am constantly wrong. A simple example would be the exam paper solution says that:

P_2(1) = 0.41483 where this describes the probability that I am in stage 2 at time 1.

When I derive this probability i get the following:

1 – ( 1 – exp (-0.25)) – (1 – exp (-0.75))

Where 0.25 and 0.75 are transition intensities which is not equal to the exam papers value. Could you please explain why?

My guess is that I must be wrong in my approach because I am operating in a multiple transition world hence I cant do this simple approach and therefore must use this differential equation approach shown in the notes? Or have I just made some silly equation error.

 

[mugono]

Hi,

I was wondering if you could help me to understand these two questions.

9(iii). I always seem to get the values of shares/cash with the opposite signs. If I want to hedge a call option do I not want to have -2600 shares, this will give me a negative delta which will cancel the call option delta? Why is it positive in the solutions?

It would depend on whether you purchased or sold the call option.

A long call option is long delta: you would need to sell stock to neutralise the portfolio delta.
A short call option is short delta: you would need to buy stock to neutralise the portfolio delta.

 

[Helloall]

I would agree with what you say.

The confusing thing in the exam paper solutions i feel is that when they say hedging portfolio they actually typically mean replicating portfolio (I dont know why, they just do).

To determine a "hedging portfolio" as defined in the exam papers they typically create a portfolio of cash and shares which replicates the value and delta of an option.

However this is not correct i think. This portfolio replicates the option, but it dosent hedge against your option position (if anything it magnifies it). An actual hedging portfolio would be the negative of a replicating portfolio.

Does this make any sense, anyone else feel the same way?

 

[Helloall]

I also dont quite understand 6 (ii) and (iii) in this paper could someone please explain? Is this something that would expected in the new format?

 

[mugono]

I would agree with what you say.

The confusing thing in the exam paper solutions i feel is that when they say hedging portfolio they actually typically mean replicating portfolio (I dont know why, they just do).

To determine a "hedging portfolio" as defined in the exam papers they typically create a portfolio of cash and shares which replicates the value and delta of an option.

However this is not correct i think. This portfolio replicates the option, but it dosent hedge against your option position (if anything it magnifies it). An actual hedging portfolio would be the negative of a replicating portfolio.

Does this make any sense, anyone else feel the same way?

I've just taken a look at the question you reference (Q9(iii)).

The question is asking you to calculate the hedging portfolio in shares and cash for 5000 call options. The examiners are assuming that the insurer / investor is long the call options and that you are hedging the positive delta on the calls.

A replicating portfolio is a special case of a hedging position: where the payoffs perfectly offset regardless of how the share price might evolve over time. This isn't the case here because a movement in the share price will change the delta on the call options whereas the delta of the shares will not change.

I think you would have scored full marks if you had assumed you were initially short calls (and long shares). In this scenario, you would have collected the premium from selling calls, which would have reduced the cost basis of buying the stock.