# Pricing of a barrier reverse convertible in python with monte carlo simulation

I'm a finance student and try to do the pricing of a given barrier reverse convertible. This has to be done by a Monte-Carlo-Simulation in Python.

The underlying is a stock of ING Groep N.V. Strike price and Spot reverence price are the same (100%) at the beginning of the contract. They pay a 3% coupon.

There a three possible pay-off options:

1. The underling's price never touches the barrier until the end of duration: Payout of the nominal value + 3% coupon

2. The underlying's price never touches the barrier until the end of duration, but is under the strike price: Payout of the nominal value + 3% coupon

3. The underlying's price touched or went under the barrier at some time of the duration: Share issue according to subscription ratio (Nominal/Strike) --> For example: Nominal =1000, Strike = 8.753 = (1000/8.753) = 144.24654. If the share is at maturity at 5€, investor gets 144.24654 shares for 5€ per share = 721,23€ + 3% Coupon

Now I'm searching for a similar case, maybe an "instruction" how an instrument like this can be priced in python, or maybe someone already coded an instrument like this and would like to help me.

Best regards for any hints.

• These BRCs are usually simple combinations of long a bond and short a down-and-in put option on the stock, where the option premium you collect basically delivers your 3% coupon. So you need a model to value the barrier option. I'm not an expert in these products, but I think (Stochastic) Local Volatility Models should get you started in the right direction. With regards to the programming part: you could try Quantlib's Pricing engine for barrier options using Monte Carlo simulation – KevinT Jun 17 at 7:32