Q8 Apr25 Paper A v)

[sophieactrainee]

Hi there,

It says in the solution for v) that the option price will stay the same if real-world probability p increases?

But the formula for the option price is

(*) V0 = D(uu) p^2 C(uu) + 2 D(ud) p (1-p) C(ud) + D(dd) (1-p)^2 C(dd)

Where D(s) - state deflator in state s
C(s) - payoff at state s , e.g C(uu) - payoff if share price increases twice in row
p - real world prob

So if we increase p, surely the price does go up, by formula (*) ?

I am confused? Maybe they meant to ask what happens to the formula used in i) - which I guess nothing happens as it is the same answer if you use the q-world formula: V0 = exp(-2r) [ C(uu) q^2 + C(ud) 2*q*(1-q) + C(dd) 2*(1-q)^2 ] ?

 

[Mark Willder]

Hi there,

It says in the solution for v) that the option price will stay the same if real-world probability p increases?

But the formula for the option price is

(*) V0 = D(uu) p^2 C(uu) + 2 D(ud) p (1-p) C(ud) + D(dd) (1-p)^2 C(dd)

Where D(s) - state deflator in state s
C(s) - payoff at state s , e.g C(uu) - payoff if share price increases twice in row
p - real world prob

So if we increase p, surely the price does go up, by formula (*) ?

I am confused? Maybe they meant to ask what happens to the formula used in i) - which I guess nothing happens as it is the same answer if you use the q-world formula: V0 = exp(-2r) [ C(uu) q^2 + C(ud) 2*q*(1-q) + C(dd) 2*(1-q)^2 ] ?

Hi Sophie

The solution is correct. The real world probability has no impact on derivative prices. Yes we multiply by p in the equation you state. But we also divide by p in this equation (as the deflator includes a term that divides by p). So the real world probability cancels out.

Best wishes

Mark