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I think both of these points are points of possible ambiguity, as has been witnessed in past papers. My advice would be to do something sensible...

Yes, that sounds sensible but careful not to fixate on mu being a thing. I don't think you are but, just in case, recall this thread......

Can you be more specific? Your post is not a million miles away from "Please teach me the course material from scratch" What have you done so far...

Yes, this is a nice summary

This is the kind of problem you can get if you try to apply a set equation as THE method for doing something, when it’s really the logic behind...

There are ALWAYS two portfolios with these. Portfolio A is always... a) one long forward and b) cash Ke^-rT This is guaranteed to deliver one...

Hi Ray, Can you please post these questions separately? Cheers, John

Yes, this is all fine. You will get different answers depending on the units you use. In fact, because the Lagrangian function is a mixture of...

I think your approach is going to work, you just need to adjust your drifts. mu = r, good but then this drift needs adjusting to r - 0.5*sigma^2...

The interpretation of S15 Q5(iii)(b) that is consistent with the Course Notes is to think that there’s a 95% chance that the value of the...

The situation is entirely analogous to being asked to solve a quadratic by using THE quadratic formula (an ill defined question in itself if we...

It's often the case that our ASET solutions provide the necessary explanation and detail that is sometimes missing from the Examiners' solutions....

Should be exact. I just checked in Excel and all 3 portfolios have a value of 1.06215001. You need to discount the cash and you've got the signs...

All of this sounds extremely good. Particularly pleased to hear about the proactiveness in your investigative approach - it's how we learn maths,...

I've corrected the mistake for adding the underlying to achieve a slope with puts

I'd made a mistake in the "CM2 position diagram tips" pdf with the underlying slope for "Puts from the right" - now corrected

I'm looking at our ASET for this question and can't see either of these numbers anywhere??

Try some numbers in Excel - this will be good practice in any case. Get a pen and place it on a piece of paper on the left. Get a friend to...

Molly, I think you mean "since no value of t gives a greater probability than at time 0, and by your response it seems that for P[ruin BY time T]...

Hi Alfie, d/dK D(a) = 0 since D(a) does not depend on K. EMM = equivalent martingale measure (a different name for the risk-neutral probability...

This hits upon one of the crucial points of Ruin theory to understand and why it is quite hard for the Examiners to set a meaningful question on...

You can do everything with calls from the left or puts from the right - check out the attached, see if it helps

When we price, we must do so under the risk-neutral probability measure Q - otherwise we will allow an arbitrage opportunity. Under Q, all risky...

Hi Bernadette, A call option means we are maybe paying K and getting the share, S. If dividends are paid, the value of the share S will go down,...

Yes, sorry about that - good spot!

James, My advice is to give Ito's lemma a miss and just use Taylor's formula (which is effectively using Ito's lemma). My advice is completely...

See attached. The September 2014 question had a mistake in it, which won't have helped. Often our ASET solutions provide the necessary detail...

Yes, GBM and cts time logN model are the same model, we just need to be careful what we mean by "mu". If we start with dSt = St (mu dt + sigma...

dWt=1dWt+0dt is merely an observation. It's just saying that, trivially the drift = 0 and the volatility = 1. Imagine that all fields consist of...

Yes. This is one of the results of the CAPM. I would phrase it more the other way round... For a portfolio to lie on the CML, its composition...

The question says that the portfolio "is equally weighted in the five assets and the risk-free asset." The market capitalisations are not John

Start with put-call parity. Differentiate twice. Delta(call) = Delta(put) + 1 and Gammas are equal. Go from there and get back to me if this...

Alfie, This material has been removed from the 2024 course. https://acted.co.uk/asset/Docs/2024/CMP%20Upgrade/CM2%20CMP%20Upgrade%202024.pdf John

Hi Molly, I can't see the 27.94 and 12.9 anywhere in our ASET solution, I really have no clue as to where they come from?? There is an...

Careful - there is no payoff at time 1. The option value at time 1 (at the 150 node) is the payoff from time 2 (187.5-4-120 = 63.5) multiplied by...

Most of the syllabus wording changes are going to be just that - wording changes. We can't know for sure what's going through the examiners'...

This bit is cash accumulating to 10% to make sure that the floor is 10%. The principle of the hedge can be achieved in many different ways: long...

Whilst it is true that the examiners would also have accepted 800*(1-7.1669%), this alternative does not match with the definition of VaR in the...

You'll end up with the same answer either way - you can use Taylor's formula on any function you like. I would argue that they're not "different...

Molly, Make sure that the time period (delta) corresponds with the period of the interest rate. If your interest rate is per annum, you need to...

In the solution to what? I can't find the words "combining all" anywhere in Chapter 7, and Section 2.2 is... Definition of the Wiener process...

You can use any calculator in the world (including Excel) to work out P[Z< number]. You do not need to use a printed table and linearly...

First we fix the first claim at time t. So, we say that it is definitely happening at time t. The trick is that the only way we can be ruined...

We can verify that W*(t) = t W(1/t) is a standard Brownian motion by showing it has: - 0 mean - normally distributed increments - cov(W*(t),W*(s))...

Increasing absolute risk aversion means that investors are more risk averse about an absolute amount of money as they get wealthier. So, a...

Hi Brett, A nice way to think about VaR (5%) is that it tells us how much we lose if the 5th worst outcome out of 100 outcomes occurs. Both...

Well done, Laura! Looks like you've sorted this? John

Hi Donie89, We've made a number of improvements to it so I would make sure that I'm looking at the latest version, Good luck! John

Hi AJL, You can do it in different ways, but it's more common to split into evenly grouped blocks according to time. Make sure you can do both...

Do EVERYTHING in your script, signpost your exam, comment, loads of #s etc. Then at the end, run the lot and copy/paste your console into Word....

Hi Bobby, It is 'so' by inspection. dBt = something * dt + something else * dBt How do we make the LHS = RHS? Well something = 0 and something...

P-lambda is a probability measure. A probability measure is an equivalent martingale measure if the discounted value of all assets is a...

This is really a question for the IAI. It might depend on the subject/paper. For example in the IFOA exams, CS2A is NOT open book but CS2B is....

Vince, I don't think the original wording is very good, it seems to be comparing a monetary amount with a probability. So, I think all...

Hi Pete, Easy answer... Yes, just learn them. If you see geo BM, eg dFt = 27Ft dt +4 Ft dZt, always start with d(ln Ft). If you see OU...

I think you've answered your own question! :-) We observe the opposite to what you "would have thought". The market is not reacting enough to do...

Hi addial, Timothy Johnson seems to work at Heriot-Watt university, so you could maybe contact them and try to find out how you get in touch with...

Hi MoleMan, I don't think you need to worry about general statistical results to do this question. We need E[T0], so we integrate tp0 from 0 to...

They look a bit mixed up. In the real world When we start with the SDE dSt = St {mu.dt + sigma dZt}, we get the solution... ln(St/S0) ~ N[...

It should be deducted when the question says it's deducted. Have you got an example?

Hi MoleMan, When I first read your post, my initial reaction was that you were just being pedantic - play the game, one item of data is censored,...

1 - sum of (aq) (If you aint left, you still there) Good luck! John

Hi Sarah, The annuity bit is good but the lump sums look a bit confused. Easiest way to do at least one of them still alive is 1 - both dead = 1...

Try some values of k. If they die in the first year, what is k? What is F(1)? Does this make sense? If they die in the 2nd year, what is k?...

The first payment is 5,000 in one year's time. PV = 5,000/1.04 The second payment is 5,000*1.04 in 2 years' time. PV = 5,000/1.04 The 3rd...

Bid/offer spread and allocation rates are applied to the original premium. eg if the allocation rate is 97% and the bid offer spread is 5%, this...

Have a think about this. What is the extra surrender cost? What is the extra maturity cost? Is it actually a cost? Or do they get the bid...

Hi PrideW, The Black-Scholes PDE is given on page 46 of the Tables, just swap the f for a g. The boundary condition is DT = g(ST,T) The...

No, as t tends to T... when S < K, Phi (- infinity) = 0, so you get 0 - 0 = 0 when S > K, Phi ( infinity) = 1, so you get S - K when S=K Phi(0) =...

It's actually very clever how you get the maximum, it uses the fact that ln(S/K) > 0 when S > K and < 0 when S < K. I'd give you that as another...

In the version I have in front of me, there are tildes on top of both Zt and ZT. Is that an e-version you have? Or has the screenshot above...

Hi Harashima, It's used to sign off derivative formulae, subject to the relevant boundary conditions... eg 1. I propose that f(St,t) = cos(St)...

Hi Harashima It doesn't really matter whether we use a bar or a tilde, the important point is that we have the behaviour of Zt under Q. So, ZT -...

Hi Harashima, The VaR corresponds to the maximum x, such that P[X<x] <10% P[X < 5] = 0.0963 < 10% P[X < 6] = 0.1912 > 10% So, x=5. Because this...

Yes, in fact, this is a good example of processes that have the Markov property but DO NOT have independent increments. A process with...

Hi Rajat, I'm not familiar with the IAI papers but I know that there are no past papers in CT7 and CT8 in the UK where the examiners wanted you...

Hi Rajat, The only connection here is through the word "systematic" having a meaning in English, otherwise we're talking about 2 different topics...

Hi Akansha, It tells you the axes in the question. Probabilities are between 0 and 1 for the y-axis, the x-axis is the number of times the car...

Yes, always try and show your working in the CT4 exam. Be efficient though. You need to open yourself up to the maximum number of method marks...

Hi Rajat, Can you please post questions on different topics as different posts? It's more helpful if people want to follow the trail of one of...

Hi Cookie, Chapter 16, Section 1.4 Example: the Black-Scholes formula for a call option In the proof, look at the second integral - this is...

Hi Cookie, In the BS formula, Phi(d2) = PQ[S(T) > K] John

Hi kartikact, These are based on our original simultaneous equations. The first equation here is: 2a + 3b + 100r = 0 which is based on the...

Hi Bharti, It's not a constant. If he earned £40,000 over the previous year then this will have been 1/4 * salary until pay rise + 3/4 salary...

Hi Kunjesh, Mmm... I see what you mean. I think I'm starting to agree with you that the question doesn't make sense to begin with! Even with...

Hi Kunjesh, Yes, you're right, with that formula, we must have lambda > 1/60, or mu could go negative. We can see this make sense again when we...

Hi Kunjesh, Can you please give the actual question? I agree a negative force of mortality does not make sense by itself. It sounds like a...

Wow, what a great question! He has 300 Rs and needs to get to 800 before 0. Easier to work in units of 100 Rs, he has to get to 8 before 0. I...

Hi Stefania, Your second question has nothing to do with the first one. It's worth posting separate questions as new posts in the future. A...

Hi Mayank, Which question are you talking about please? John

Hi akashgoy, Basis risk example Let's say we have entered a receiver swap to hedge some particular liabilities. So, we receive fixed interest...

Hi forza_bologna, There isn't really a reason to expect the l values to be any way round particularly, it's not important. The l values are just...

Hi akashgoy, Yes, that's precisely it. You've already answered your own question (very well!). If we are hedging interest rate changes using a...

The question says... Mortality experience: 80% AM92 Select So, look up the values in Tables and multiply by 0.8. I've noticed nad07 that you...

Prob of maturity (ie not dying) * 10% * Fund at end =(1-0.003539)*0.1*2,657.96 = 264.86 This is a cost Good luck! John

I'd probably buy mini ASET to top up with the latest paper. It's only £12 (our website doesn't mention adding VAT either)...

Not if the question is at 6%. Page 106 of Tables, figure's there. ALWAYS perform 3 checks in your head when you look up one of these from...

Hi nad07, Reserves - same advice really... I've shown you exactly how this works on Question 13.10, so have another go yourself with this one......

Hi nad07, I can't see where you're getting your numbers from but I suspect that you're not multiplying INDEPENDENT probabiulities together. In...

Hi nad07, Reserves - same advice really... I've shown you exactly how this works on Question 13.10, so have another go yourself with this one......