Risk Management - facts and formulas

Question 1

Delta of a put or call? (Forumula)

Answer 1

1. d1 - Sedan finns N(d1) värdet (kan krävas interpolering). Ta sedan N(d1)-1 för att få svaret.

Question 2

What do a Delta of an option tell you? (Value)

Answer 2

“When the asset price go up with 1 so will the value of the option decrease with one”.

Question 3

Gamma ? (Formula)

Answer 3

It means when the asset price rises by one unit, 𝛥 of the put option rises by the calculated gamma. NOTE: A linear product has a gamma of zero.

Question 4

Vega? (Volatility)

Answer 4

It means when the asset price volatility rises by 1%, the value of the put option rises by the calculated Vega

!!(OBS! If your calculated Vega is 3 - it means that the value of the put option raises by 0,03)!!

Question 5

Theta for a put and a call? (Time)

Answer 5

-The theta of a portfolio is the rate of change of the value of the portfolio with respect to the passage of time, with all else remaining the same.

-Same formula but for a put-option you take -d2 instead of d2.

Question 6

Rho? (Interest)

Answer 6

The rho of a portfolio is the rate of change of the value of the portfolio with respect to the level of interest rates.

Question 7

What about Portfolios? (Delta, Gamma, Vega)

Answer 7

In practice, portfolios can become frequently delta-neutral, but to become gamma- and vega-neutral is difficult and not always possible.

Question 8

Expected Short Fall?

Answer 8

Y = -0,5

Question 9

VaR?

Answer 9

Get the value from the Normal Distribution table. Remember to take the negative value.

Question 10

First and second condition when dealing with insurances? (Full insurance vs. Partial)

Answer 10

1st: The high risk consumer most have a higher utility of being full insured compared to pretending be a low risk consumer and wanting the partial insurance.

2nd: The low risk consumer has to have a higher utility of being partial insured compared to being fully insured. Calculate using the first F* of being fully insured (with the rate 0,2F) and compare in with the new F in the formula with 0,1F and 0,9F.

Question 11

Black and Scholes for Put and Call option (and d2) ? (after you’ve calculated d1 and d2).

Answer 11

d2 = d1 - (σ * sqrt(T))

Put = (e^-rT)(KN(-d2))-(S*N(-d1))

Call = SN(d1) - (e^-rT)*KN(d2)

Question 12

l’Hopital’s rule?

Answer 12

The rule states that if the limit of the ratio of two functions f(x) and g(x) as x approaches a particular value c is of the form 0/0 or ∞/∞, then the limit of the ratio is equal to the limit of the ratio of the derivatives of f(x) and g(x) as x approaches c, provided that the latter limit exists and is not equal to 0/0 or ∞/∞.

Question 13

GARCH Model?

Answer 13

The GARCH (Generalized Autoregressive Conditional Heteroscedasticity) model is a statistical model used in finance and economics for modeling and analyzing time series data, particularly for modeling the volatility of financial time series.

The basic idea behind the GARCH model is to capture the time-varying volatility of financial returns by modeling the conditional variances as a function of past values of the residuals and past conditional variances. In other words, the GARCH model assumes that the volatility of financial returns changes over time, and it tries to capture this change by using lagged values of the residuals and conditional variances in the model.

Question 14

Interpolar

Answer 14

(H-L) / (d1-L) = (Ht - Lt ) / (x-Lt)

• Re-arrange the order so X is free. Calculate.

H= Högst värdet
L = Lägsta värdet

Ht =Högsta värdets tabellvärde
Lt = Lägsta värdets tabellvärde

Question 15

N’(d1) = ?

Answer 15

See pic.
1. E funktionen: Lägg allt inom parentesen och höj bara upp d1-värdet till 2)

2. Dela med SQRT(2pi)