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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...
OK, let's do Year 2 and you can do the others. I've copied and pasted my advice from above, so that you can see exactly how it applies to...
Member is 30 with 10 years of past service. So, when he is 60, he will have worked for 40 years. 50% = 40/80 and so this is where the maximum...
If you make a silly mistake, not only is it an automatic fail - you will also be taken from the exam room and dealt with by a firing squad. Or,...
This is always a stumbling point... Profit vector = profits at end of year per pol in force at START OF THAT YEAR. So, if we are in year 3,...
Hi Jolien, I think this question is still fair game. In CT5 we cover cashflow approaches towards profit testing, whilst when valuing pension...
Further to this, please check out this forum post, where I explain where the probability comes from in Sep 2007 Q9......
This question looks like you need a bit of knowledge of the scoring in tennis, which isn't great for a CT4 exam, we shouldn't be examined on our...
It's really good that you've made this algorithm and thank you for sharing it with everyone! John
It's important to realise that periodic is where a return from a state to itself is ONLY possible in a multiple of k>1 steps. If a Markov chain...
Hi Suresh, The second line is replacing Xn with Xm plus the steps Y between times m and n. X is a process that adds up the Ys The third line has...
Hi deepakromore, This is often confusing for students because why is there a cost of life cover when nobody has died yet? it is a bit weird...
To get a_ you need to convert from adue... a_xy:n = a_xy - v^n npx a_x+n:y+n TIP : put the CT5 discount factor v^n npx in your memory button,...
Time is the main enemy in CT5, so the rewards are there on exam day for the people who've been doing the most practice. It doesn't matter how...
Something to be careful of here, a very common mistake in CT5, is to forget the survival benefit. A_30:10 = A_30 - v^10 10p30 A_40 + v^10 10p30...
Hi Adithyan, Because this question is a bit different to the point of the original post already answered by Mark, we've answered it in your other...
One method is to start with the probability that the game returns to Deuce given that the game is currently at Deuce. This is 0.4*0.6 +0.6*0.4 =...
Have you got a specific question? Often a process has independent increments by assumption. Other times, you need to calculate the increments...
We should be asking ourselves whether the number of signs is correct. So, with 20 age groups for example... if we had 4 positives, we should be...
The question will tell you the state space. Have you got an example question from the UK exams or the ActEd CMP that you find difficult to...
Calendar year and policy year rate intervals are not in the CT4 syllabus so this question could not be asked on the UK CT4 paper. If the...
Generally, the chapters are put there to be read, not to be skipped. For the UK CT4 exam, skipping Chapter 5 would be a disaster John
This is the same method, your method is very sensible John
Hi Deepak, Yes, well done, this seems to get to the correct answer! John
If an event happens some time over a 3 month period but we don't know when, it is sensible to assume that it happens in the middle of this 3-month...
Hi Ujjwal, Yes, well done, these are the exact two examples I was thinking of. I would talk about both these features of human mortality if I...
Sum across the possible paths from Level 1 to Level 4... the probability of this path * the time taken for this path to happen
Yes, this approximation is fine. When you go from ISD test to Chi-squared test, you can simply square all the Zs Good luck! John
Just as a general tip, if you're looking at an exam question and asking if it's possible for this question to come up in the exam, I would tend to...
If someone retires due to ill-health, their pension is calculated and they start to receive their annuity. If they later recover from their...
We should use a continuity correction here because we are going from a Bin(25,0.5) to a Normal(12.5, 6.25) We have observed 18 positive signs and...
In reality we usually find that the force of mortality increases with age. Note that this is not always true. Please give two examples where...
500 toys start at 9am, time 0 12 fail (die) at time 4, 1pm. 17 censored at time 10, 7pm 25 fail (die) at time 11, 8pm 3 censored at time 13, 10pm...
Hi deepakraomore, Have you got ASET or the Revision Notes? I strongly recommend CT4 ASET for really helping you answer the questions on the last...
Hi Deepak, It's important that we give time for all CT4 students to reply to each others' posts. Unfortunately, you don't seem to have had too...
This is in the Core Reading. Best to reflect this in your exam script, Good luck! John
1. Up to you, the sum from n=1 to 10 of n is the same as the sum from n=11 to 20 of (n-10) 2. the probability of any continuous random variable...
this is showing that when we jump, the state we go has nothing to do with how long we've spent where we are. eg stay healthy for 10 years, leave...
Tutor says "I agree". What student says on this?
There's no point dividing the number of deaths on Tuesday by the number of people in the room on Monday. We want to divide the number of deaths on...
Because this is the difference in their definitions. Both sum b-a across censored lives, no difference Initial EtR sums 1-a across deaths, central...
The mortality of EACH life follows the binomial model. The prob that a life survives is 0.8^10 = 0.10737. So, prob a life dies is 1 - 0.10737 =...
I don't know what question you are talking about but I suspect the answer is that one laptop is censored before that time. Either because it...
In the naive binomial model, we have D ~ Bin (n,q) but this assumes everyone is observed from x to x+1 In fact, some lives join at age x+a and...
Here the death data is the Day Qualified and the censored data is the Day Left Without Qualifying Good luck! John
It would have to be a without profit policy. Realistically, the main occasion to worry about it is in a profit testing question for a standard...