Symbol

Definition

L(t)

Bank loan at time t

μ(t)

Growth rate of bank loan

M

Multiplier

e^−rT

Continuously compounded discount factor

σ_L(t)

Volatility of bank loans at time t

D(t)

Bank deposits at time t

μ_D(t)

Growth rate of bank deposit at time t

σ_D(t)

Volatility of bank deposit at time t

W₁

Standard Brownian motion from the dynamics of loan

Bank value at time t

Long-term average volatility of variable cost

W₃

Standard Brownian motion from the source of growth rate in loan

W₂

Standard Brownian motion from the dynamics of deposit

Volatility of growth rate in loan at time t

Volatility of growth rate in deposit at time t

k

Mean reversion coefficient

Risk premium

r_f

Risk free rate

Beta of the market

R_m

Market risk

C(t)

Total cost at time t

Variable cost at time t

F

Fixed cost

Long term average of variable cost

Volatility of variable cost at time t

W₄

Standard Brownian motion associated with growth rate in deposit

W₅

Standard Brownian motion associated with variable cost

Other sources of bank income

r

Interest on loan

s

Interest on deposit

Y(t)

After tax net income

X(t)

Cash balance at time

Dep

Depreciation

P

Accumulated property plant and equipment

Capx

Capital expenditure

DR

Percentage of depreciation

V(t)

alue of bank at an arbitrary time t

V(0)

Value of bank at present time

E_Q

Equivalent martingale measure

Corporate tax rate