Update README.md

Author: GregorFabjan

vasicek_two_factor/README.md

@@ -4,20 +4,20 @@
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 </h1>
 
-A simple model for calculating the nominal interest rates. Used to add inflation to the simulation of interest rates. The model has two sources of randomnes (Two correlated Brownian motions)
+A simple model for calculating the nominal interest rates. Used to add inflation to the simulation of interest rates. The model has two sources of randomness (Two correlated Brownian motions)
 
 ## Problem
-When modeling the nominal rate, both the real rate of return and the inflation should be considered. The correlation between them means that one should use a multifactor model as opposed to two independent models. Additionaly, there is a robust body of literature showing that both real rates and the inflation are mean-reverting
+When modelling the nominal rate, both the real rate of return and the inflation should be considered. The correlation between them means that one should use a multifactor model as opposed to two independent models. Additionally, there is a robust body of literature showing that both real rates and the inflation are mean-reverting
 
 ## Solution
-The simplest model for modeling real rates and inflation together is the multifactor Vasicek model https://en.wikipedia.org/wiki/Vasicek_model. The Vasicek model is a short rate model describing the evolution of rates. Both the real rate process and the inflation rate process are assumed to follow a Vasicek model. The movement of the two curves is given by a two dimensional correlated Brownian motion
+The simplest model for modelling real rates and inflation together is the multifactor Vasicek model https://en.wikipedia.org/wiki/Vasicek_model. The Vasicek model is a short rate model describing the evolution of rates. Both the real rate process and the inflation rate process are assumed to follow a Vasicek model. The movement of the two curves is given by a two-dimensional correlated Brownian motion
 
 ### Input
 Vasicek model simulator:
  - `r0` ... Starting annualized real rate and inflation rate. ex. if the annualized real rate is 1.4% and inflation is 6%, then r0 = [0.014, 0.06]   
  - `a` ... mean reversion speed for the real and inflation process. ex. if the reversion factor is 0.8 for real rates and 1 for inflation, a = [0.8, 1]         
- - `b` ... long term mean level for the real and inflation process. ex. if the long term real rate is 1% and long term inflation is 1.5%, b = [0.01, 0.015]    
- - `sigma` ... instantaneous volatility of the real and inlfation process. ex. volatility of the real rate process is 5% and inflation process is 4%, sigma = [0.05, 0.04] 
+ - `b` ... long term mean level for the real and inflation process. ex. if the long-term real rate is 1% and long term inflation is 1.5%, b = [0.01, 0.015]    
+ - `sigma` ... instantaneous volatility of the real and inflation process. ex. volatility of the real rate process is 5% and inflation process is 4%, sigma = [0.05, 0.04] 
  - `rho` ... correlation between the stochastic noise that generates the two processess. ex. if the calculated correlation coefficient is 0.t, rho = 0.6            
  - `T` ... modelling time horizon. ex. if time horizon is 25 years, T = 25               
  - `dt` ... time increments. ex. time increments are 6 months, dt = 0.5             
@@ -33,7 +33,7 @@ Vasicek model simulator:
  - `interest_rate_simulation` is a pandas dataframe with one sample path generated by the model. One for the real rate process and the other for the nominal rates (real rate + inflation rate)
 
 Vasicek model pricing:
- - Price of a zero cupon bond with maturity T based on the model. The technique used is Monte Carlo with 1000 scenarios and numeric integration
+ - Price of a Zero-Coupon Bond with maturity T based on the model. The technique used is Monte Carlo with 1000 scenarios and numeric integration
 
 Vasicek model calibration:
 TBD
@@ -68,7 +68,7 @@ interest_rate_simulation.plot(figsize = (15,9), grid = True)
 plt.legend()
 plt.show()
 
-# Vasicek model pricing of a zero cupon bond
+# Vasicek model pricing of a Zero-Coupon Bond
 nScen = 1000
 zero_coupon_bond = ZeroCouponBond(1)
 zero_coupon_bond.price(r0, a, b, sigma, rho, T, dt, nScen)