deriva1.clj

(use 'com.lambder.deriva.core)

(def N 
  '(/ 1
      (+ 1
         (exp (- 
                (* -0.07056 (pow x 3))
                (* -1.5976 x)))))

(def d1 '(/ (+ (/ F K) (* T (/ (sq sigma) 2)))))

(def d2 '(/ (- (/ F K) (* T (/ (sq sigma) 2)))))

(def call
    `(* 
        (exp (- (* r T))
        (- 
          (* F ~(bind N x d1))
          (* K ~(bind N x d2)))))

(def put
    `(* 
        (exp (- (* r T))
        (- 
          (* F ~(bind N x (- d1)))
          (* K ~(bind N x (- d2))))))

(defn black-expression [call?] call put)


;; usage

(def black-model-with-sensitivities (∂ (bind (black-expression true) T 0.523) F K r))

(black-model-with-sensitivities 12.3 14.3 0.03)
(black-model-with-sensitivities 12.3 11.0 0.03)
(black-model-with-sensitivities 12.3 11.0 0.02)