Pricing Deposit Insurance
Table of Contents
1 Overview
Merton (1977) used option pricing methods to value deposit insurance.
2 Deposit Insurance
Banks deposits are insured by the Federal Deposit Insurance Corporation (FDIC).
3 Option Pricing Model
Let \(D\) and \(A\) stand for the value of the bank's deposits and assets. Then the payment to the bank be the deposit insurer is \(max(D - V, 0)\). That is, if the value of the banks assets are less than the deposits, then the insurer must pay:
\[D - V\]
However if the bank's assets exceed deposits then the insurer pays \$0.
3.1 Original Black-Scholes-Merton Model
3.2 Margrabe Spread Option Model
4 Data
Extract only Granville Bank.
import pandas as pd data = pd.read_csv("callreports_final.csv") data = data[data.rssdid == 560830] print(data.shape) print(data)
(152, 167)
rssdid chartertype ... intincreloans dividendoncommonstock
804718 560830 200 ... NaN NaN
804719 560830 200 ... NaN NaN
804720 560830 200 ... NaN NaN
804721 560830 200 ... NaN NaN
804722 560830 200 ... NaN NaN
... ... ... ... ... ...
804865 560830 200 ... 168.0 17.0
804866 560830 200 ... 157.0 15.0
804867 560830 200 ... 158.0 15.0
804868 560830 200 ... 157.0 16.0
804869 560830 200 ... 159.0 16.0
[152 rows x 167 columns]
print("hello world")
5 Python Implementation
Below is a function which will calculate the latest cost of deposit insurance for a given bank.
def get_cost(idrssd): """calculate the value of deposit insurance for a given bank using the approach of Merton (1977)"""" ## first calculate asset volatility
6 References
@article{merton1977analytic, title={An analytic derivation of the cost of deposit insurance and loan guarantees an application of modern option pricing theory}, author={Merton, Robert C}, journal={Journal of Banking \& Finance}, volume={1}, number={1}, pages={3–11}, year={1977}, publisher={Elsevier} }