Answer the below questions in 500 words each and use mathematical proof where required.
Explain MLE and its application in quant finance problems.
Explain different between OLD and MLE and take the case of Regression and logistic regression to explain both methodology
Prove scaling of standard deviation sd=sd(t)^.5
What is the difference between clean and dirty price for a treasury security, refer some links online.
Explain the difference between modified and ‘Macaulay duration’, derive one from the other.
Calculate duration using annual and continuously compounded rates.
Explain why GBM or the models used in Equity cannot be used for interest rate modeling. Give example and explanation of interest rate models. What interest rate models are used for short and long term.
If you have two biased coin one gives 50% and 70%. You pick one and gets 60%, which coin have you picked. Can you solve this using MLE.
Which yield to rate in duration – what will happen if you use annual vs compounded rate for MacD/(1+y)