Retirement benefits:

I dont fuly understand the pension plan assumptions:

Why does discount rate affect pension liability and how (liability or asset)

How does risk free rate or interest rate affect options

Thanks !

Retirement benefits:

I dont fuly understand the pension plan assumptions:

Why does discount rate affect pension liability and how (liability or asset)

How does risk free rate or interest rate affect options

Thanks !

20 days from exam … wow, you are really great.

The PBO is simply a present value calculation that relies on the assumed discount rate. So, the discount rate has a direct impact on how large or small the PBO is at any given period and thus the overall funded status of the plan.

So, a higher discount rate reduces the PBO and increases the funded status of the plan (i.e. you have a smaller net pension liability or a larger net pension asset, depending on the situation). A lower discount rate has the opposite effect, obviously.

Hope that helps.

**See below**

**Simply:**

Q: Why interest rates affect pension costs

A: A net pension expense (net pension income is possible) includes:

- Expected return on plan assets (income).
- Service costs for benefits earned (additional service provided).
- Interest costs on benefit obligations (passage of time) (that’s why interest rates affect pension costs)
- Other “smoothing adjustments”.

This amount is reported on the income statement, usually as an “other income or expense”. However these numbers do not record economic reality.

Q: How does risk free rate or interest rate affect options?

A. The Black-Scholes-Merton formulas for the prices of call and put options are:

c = S_{0} N(d_{1}) - X e ^{-rcT }N(d_{2}) p = X e ^{-rc T} [1 - N(d_{2})] - S_{0}[1 - N(d_{1})]

where: d_{1} = {ln(S_{0}/X) + [r^{c} + (σ^{2}/2)] T} / [σ (T^{1/2})]. d_{2} = d_{1} - σ (T^{1/2}).

r^{c} = the continuously compounded risk-free rate of return. (assumed constant in Black-Scholes-Merton formula)

As noted above, Black-Scholes-Merton formula assumes a fixed interest rate. However one can assess how an option price would differ if the risk free rate is changed ie RHO and the following are key to note:

- Large changes in the interest rate have relatively little impact on the option prices. That is, the price of a European option on an asset is not very sensitive to the risk-free rate.
- For a call option, rho (RHOc) is always positive. For a put option, rho (RHOp ) is always negative.
- Both RHOc and RHOp are reduced to zero as time passé and we get to expiration

hey, heres a quick way to think about how interest rates impact call and put prices… not really an intuitive answer, but if you get the question on the exam…

for binomial trees:

risk-neutral probability of an upward move is:

((1 + r) - d) / (u - d)

lets give these numbers

r = 5%

u= 1.2

d = 1/1.2 = 0.833333

therefore the risk-neutral probability of an up move is

((1 + 5%) - 0.833333) / (1.2 - 0.83333333)

= 0.59%

this is the “weight” you will assign to all upward movements in the tree

now we all know that if you assign a higher value to an upward move, and call prices are more valuable when the stock moves up, a higher probability assigned to an upward move will increase the model’s price for call prices and decrease the model’s price for put prices.

now assume that interest rates increase to 10%, and solve the risk-neutral probability of an upward move.

you will notice using the above formula the probability has increased from 0.59 at 5% to 0.73 at 10%

we are assigning a much larger probability to the upward move when interest rates increase, when will increase the value of call options and decrease the value of put options.