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DamienF
Topic Author
Posts: 14
Joined: April 9th, 2014, 8:42 am

### determining the future value of a put option

Ive been asked to do an analysis of change (in value) exercise for our Ftse100 put option holdings from end 2012 to end 2013. One of the steps is to move to an end 2013 date but with end 2012 market conditions (MC), e.g. use the 1 year forward curve for discounting etc. The bit I'm stumped on is what I should use for the 2013 date spot ftse100 from 2012 MC. I'm using the classic black scholes formula for valuation. Someone suggested to me using the 2012 1 year forward price for ftse 100 but I'm not convinced that this is correct as it does not reflect return for bearing risk. If the derivative value at t is V_t, then I would have thought the value at end 2013 using end 2012 MC would be, E[V_2013] under the real world measure, in which case I'd need to know expected spot at end 2013.

Samsaveel
Posts: 436
Joined: April 20th, 2008, 5:47 am

### determining the future value of a put option

calibrate drift and volatility based on 2012 market data,your using historical data so you are operating in the real world measure.do your simulation ,and project forward the underlying FTSE trajectory 1-year forward from 2013 start to 2013 end ,which means you are onlygenerating one Gaussian deviate per path.you will have a distribution for your FTSE at the end 2013 ,i.e N -paths.compute your Put payoff at each node as max(k-FTSE_Value_simulated,0),and average out then discount back to valuation date using the discount curve from 2013 start-2013 end.

DamienF
Topic Author
Posts: 14
Joined: April 9th, 2014, 8:42 am

### determining the future value of a put option

Thanks for your response. Maybe this is what you have answered but I guess what I'm fundamentally asking is how do I calculate the price of an option in one years time given the markets views. The put options don't expire in 2013, this is just a valuation date. An even simpler question is, what is the market consistent value of the ftse100 in one years time? Once I know that I can value the options at 2013 by discounting using forward rates derived from 2012 yield curve

Martinghoul
Posts: 3256
Joined: July 18th, 2006, 5:49 am

### determining the future value of a put option

Wait, you're just looking how to compute the 1y fwd FTSE?

DamienF
Topic Author
Posts: 14
Joined: April 9th, 2014, 8:42 am

### determining the future value of a put option

I'm using the classic black scholes formula. Ignoring dividends for the moment, say I want to calculate the price of a put option today then I can use spot ftse, today's yield curve and today's volatility for the term and strike of the option. OK, now I want to know what the price of this option would be in one years time using prevailing markets conditions. I can use the 1 year forward curve as my yield curve as that point. If I had it I could use a forward volatility. But what do I use for the spot in 1 years time based on prevailing market conditions. I had to reduced the problem to this question.

daveangel
Posts: 17031
Joined: October 20th, 2003, 4:05 pm

### determining the future value of a put option

QuoteOriginally posted by: DamienFI'm using the classic black scholes formula. Ignoring dividends for the moment, say I want to calculate the price of a put option today then I can use spot ftse, today's yield curve and today's volatility for the term and strike of the option. OK, now I want to know what the price of this option would be in one years time using prevailing markets conditions. I can use the 1 year forward curve as my yield curve as that point. If I had it I could use a forward volatility. But what do I use for the spot in 1 years time based on prevailing market conditions. I had to reduced the problem to this question.the answer to this depends on why you need to value this contract in 1 year's time. the best estimate of the FTSE spot in 1 year is todays price with interest.
knowledge comes, wisdom lingers

DamienF
Topic Author
Posts: 14
Joined: April 9th, 2014, 8:42 am

### determining the future value of a put option

Yeah so should I use the forward price? To me I feel like the inputs into the BS formula in 1 years time, e.g. spot ftse, interest rates etc. should be those found under the real world measure. I'm wondering if this is correct?

daveangel
Posts: 17031
Joined: October 20th, 2003, 4:05 pm

### determining the future value of a put option

it may be correct but you haven't told us why you want to do this.
knowledge comes, wisdom lingers

DamienF
Topic Author
Posts: 14
Joined: April 9th, 2014, 8:42 am

### determining the future value of a put option

Thanks for your response. The task I'm faced with is that I value the put options on end 2012 market conditions (MC). I then revalue them as at end 2013 but using the end 2012 mc, e.g. discount back to end 2013 using end 2012 1 year forward yield curve. I then revalue them at end 2013 using end 2013 MC. This is meant to explain the change in value over the year. In the second step I thought that you would use an expected spot for end 2013 based on end 2012 MC rather than a futures price. I don't how I would estimate this or if it was correct

Samsaveel
Posts: 436
Joined: April 20th, 2008, 5:47 am

### determining the future value of a put option

the fact of the matter is that the task your are faced with is over your head.you are simply not making sense (MC,Market views,2012,end 2013 MC ,etc.....)what is your question in 6 words ,simples!

DamienF
Topic Author
Posts: 14
Joined: April 9th, 2014, 8:42 am

### determining the future value of a put option

At end 2012, our put options were worth X. At end 2013, they were worth Y. My boss wants an analysis of the change in value over this period. An intermediate step is to value the options at end 2013 but using end 2012 yield curves etc. This allows us to compare the expected value as at end 2013 from an end 2012 perspective against the realised end 2013 value. I want to value the options in this step. Do you now how I would do this?The put options are vanilla. Cheers
Last edited by DamienF on April 22nd, 2014, 10:00 pm, edited 1 time in total.

DamienF
Topic Author
Posts: 14
Joined: April 9th, 2014, 8:42 am

### determining the future value of a put option

If I owned a risk-free zero coupon bond paying 1 and maturing in 2 years then its value would be (1+r_2)^-2 where r_2 is the risk-free yield. Its value in one years time (from todays perspective) would be (1+f_1_2)^-1, where f_1_2 is the forward rate between terms 1 and 2. I want to price an option in this way

Posts: 94
Joined: July 14th, 2002, 3:00 am

### determining the future value of a put option

HelloIf I understand correctly you are trying to explain the change in the put value from 2012 to 2013, so essentially analysing what happened in the PAST.I would therefore recommend not bothering too much about "projecting", but rather keeping all inputs "the same" (details below) except for the valuation time.Practically:1- spot = same as in 20122- rates = same spot rate curve as in 2012 (that is the 1year rate, 2year rate, etc remain the same)3- divs = if discrete cash divs push simply "slide forward" in time and only consider divs post 2013; if div yield keep the same4- implied vol = same as in 2012Of course valuation date = 2013!! (that is your time to maturity must have gone down by a year)This will give you a new value to compare with the 2012 price: call the difference "time impact".Then start amending the above parameters (1 to 4) one by one and set them to their 2013 value. Record the increment in value at each step (call them respectively "spot impact", "rates impact", etc). Make sure you do the changes cumulatively so that all parameters are set to their 2013 value at the end of the exercise.Remind your boss you could have arbitrarily chosen a different order (for instance amending parameter 4, then 3, 2, 1) which would have resulted in different values of "spot impact", "rates impact", "divs impact" and "vol impact" (although the sum of the 4 impacts would remain the same), because the order you select determines how you allocate the cross effects.Cheers

rmax
Posts: 6080
Joined: December 8th, 2005, 9:31 am

### determining the future value of a put option

This is just P&L explain under a different name. Two traditional ways to do this: either bump each of the underlying components. So bump the spot by changing this parameter and revalue the portfolio, then change the time, then Vol etc. The other approach is after you change each parameter you then "reset" the value: so you bump spot, reval, then reset it to the initial condition and then bump time etc. You will get unexplained P&L in the second approach (unless you bump each cross).

riskneutralprob
Posts: 38
Joined: December 16th, 2005, 5:16 pm

### determining the future value of a put option

First Things First,http://en.wikipedia.org/wiki/Forward_priceI'm still not sure exactly what you're looking for. Is the 1 year option expired a year later?

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