Local volatility

<p>A local volatility model, in <a href="/facts/Mathematical_finance/P9otEltQ">mathematical finance</a> and <a href="/facts/Financial_engineering/K43H6H28">financial engineering</a>, is an option pricing model that treats <a href="/facts/Volatility_(finance)/mCdus1MW">volatility</a> as a function of both the current asset level 
  
    
      
        
          S
          
            t
          
        
      
    
    {\displaystyle S_{t}}
  
 and of time 
  
    
      
        t
      
    
    {\displaystyle t}
  
.  As such, it is a generalisation of the <a href="/facts/Black%25E2%2580%2593Scholes_model/TPPG5YWQ">Black–Scholes model</a>, where the volatility is a constant (i.e. a trivial function of 
  
    
      
        
          S
          
            t
          
        
      
    
    {\displaystyle S_{t}}
  
 and 
  
    
      
        t
      
    
    {\displaystyle t}
  
). Local volatility models are often compared with <a href="/facts/Stochastic_volatility/d5zBCcUP">stochastic volatility models</a>, where the instantaneous volatility is not just a function of the asset level 
  
    
      
        
          S
          
            t
          
        
      
    
    {\displaystyle S_{t}}
  
 but depends also on a new "global" randomness coming from an additional random component.    
</p>

Local volatility open-in-new

Local volatility