DU Finance Stock and Pricing Question


Description

Question 1

A European put liberty provides the just to vend a hoard at a pre-specified collide expense 𝐾 at ripeness conclusion 𝑇 − 𝑡. The Black-Scholes equation for pricing a put liberty is dedicated as follows (see attached" equation.png")

a) You lack to distinguish the amend expense for a put liberty after a while 26 weeks until stolidity (pretend 52 weeks in a year). The present hoard expense is 𝑆 = $20.50, and the collide expense on the put liberty is 𝐾 = $19. The hoard has an annualized disproportion of 𝜎 = 0.20 and the identical annual risk- gratuitous objurgate is 𝑟𝑓 = 0.03. What is the amend expense for this put liberty?

b) What is the expense of a ole liberty on the corresponding underlying hoard after a while the corresponding ripeness and collide expense? (Note: the ole liberty equation was granted in the Week 13 slides.) Why is the ole liberty over rich than the put liberty?

c) Suppose that you own 900 put liberty narrows, where each narrow represents 100 distributes. What is your delta posture? How numerous distributes do you want to buy or vend to complete delta indifference? For this scrutiny, you conquer primitive want to proportion the delta of a put liberty, which is dedicated as follows:

Δ = −𝑁(−𝑑1)

d) Pretend the liberty posture and delta-neutral distribute posture from disunite (c). Aftercited an rights assertion on that day, precariousness in the hoard expense skyrockets to 𝜎 = 0.40. The hoard expense, however, sediment unchanged (𝑆 = $20.50). Proportion the new delta posture aftercited this alter in precariousness. How numerous distributes do you want to buy or vend (not-absolute to your distribute posture from disunite (c)) to complete delta indifference?