Arbitrage Free Valuation

hello,

Please will you guys advise if one will be required to populate the lattice tree, or just describe the process.

You must be able to calculate the price of a bong from a lattice tree. i.e taking the final rate and coupons and working back by discounting/ adding coupon, averaging and discounting again.

This is imperative for the exam.

Freudian slip?

thanks that i am aware :+1:

I was asking about populating the lattice tree; i.e calculating the rates that are on the tree or just describing that it is an iterative process that one completes using an analytical tool such as Solver

You could have to fill in some rates on the tree. However, they would have to give you enough information that you can do so without resorting to something like Solver (which, by the way, is a numerical tool, not an analytical one).

For example, they may tell you that the volatility is 10% and that the lower rate at time 1 is 4.2%, then ask you for the upper rate at time 1; it’s 4.2% × e2(10%) = 4.2% × e0.2 = 5.1299%.

Or they may give you the lower and upper rates at time 2 as 3.5123% and 6.3998% respectively, then ask you to compute the middle rate at time 2; it’s √(3.5123% × 6.3998%) = 4.7411%. Alternatively, you can compute the volatility by solving:

e4σ = 6.3998% / 3.5123% = 1.8221

4_σ_ = ln(1.8221) = 0.6000

σ = 0.6000 / 4 = 0.1500 = 15%

then use that volatility to compute the value of the center rate.

indeed… stress levels are high you know…

Thank you Magician -----at least that I can manage, given my math skills are very raw. :open_mouth:

You’re welcome.